# solving circuits using graph theory

Hey All, W elcome to the Graph Theory Problem Solving Community . Computer Science Engineering: Graph theory can be used in research areas of computer science. Here is a graph representing a cube. Since then it has blossomed in to a powerful tool used in nearly every branch of science and is currently an active area of mathematics research. A path is simply a sequence of vertices where each vertex is connected by a line to the next one in the sequence. The NRICH Project aims to enrich the mathematical experiences of all learners. Using Kirchhoff’s laws, you can simplify a network of resistors using a single equivalent resistor. Can you draw for yourself other simple graphs which have one sort of circuit in them and not the other? Each of the following numbers is the product of exactly three prime factors and you have to arrange them in a sequence so that any two successive numbers in the sequence have exactly one common factor. When you want to analyze different loads connected in series with the source circuit, the Thévenin equivalent is useful; when loads are connected in parallel with the source circuit, the Norton equivalent is a better choice. Took Help View History 'books google co Lycos Mail Goo* Emergency Appointmew Teachers 6th Pay Re..n Faculty Salaries COMMISSION: On the NRICH website you will find a lot of problems on graphs and networks which you might like to try. Any two vertices The two equivalents are related to each other by a source transformation. The whole subject of graph theory started with Euler and the famous Konisberg Bridge Problem. After finding the node voltages, you use current-voltage (i-v) relationships such as Ohm’s law to find device currents and use the node voltages to find device voltages. That’s where device and connection equations come in. When analyzing circuits, you can simplify networks consisting of only resistors, capacitors, or inductors by replacing them with one equivalent device. If there is a path linking any two vertices in a graph, that graph … After generating the entire graph, we can see the … To get the total output, you calculate the algebraic sum of individual contributions due to each source. embed rich mathematical tasks into everyday classroom practice. Mesh equations are KVL equations with unknown mesh currents as variables. After finding mesh currents, you use i–v relationships to find device voltages. Finding the Thévenin or Norton equivalent requires calculating the following variables: VT = VOC, IN = ISC, and RT = RN = VOC/ISC (where T stands for Thévenin, OC stands for an open-circuit load, N stands for Norton, and SC stands for a short circuit load). Fundamental Loop Matrix 3. The numbers are $222$, $255$, $385$, $874$, $2821$, $4199$, $11803$ In the Peterson graph there are no Hamiltonian circuits so, unlike the Primes Puzzle above there is no way to put the cards into the required circuit. All rights reserved. To master the graph problem-solving capabilities we will be starting from the basics and proceeds to … Directed Graphs8 3. and $20677$ and we have used only the first twelve prime numbers. Thévenin/Norton equivalents: Circuit analysis can become tedious when you’re trying different loads with the same source circuit. When dealing with complicated circuits, such as circuits with many loops and many nodes, you can use a few tricks to simplify the analysis. A Little Note on Network Science2 Chapter 2. If you try to solve the puzzle by The following equations show equivalent series and parallel connections for resistor-only, capacitor-only, and inductor-only combinations. if we traverse a graph such … i m looking out for some information regarding graph theory and its application to electric networks... my circuit analysis book doesnt cover this topic.. any book or … John M. Santiago Jr., PhD, served in the United States Air Force (USAF) for 26 years. Solve this equation for the value of x: Plot the solutions to the equation y + x = 8 on a graph: On the same graph, plot the solutions to the equation y − x = 3. Using These Notesxi Chapter 1. Euler circuits exist only in networks where there are no odd vertices, that is where all the vertices have an even number of edges ending there. concepts of graph theory. Definitions Circuit, cycle. Another example could be routing through obstacles (like trees, rivers, rocks etc) to get to a location. Path – It is a trail in which neither vertices nor edges are repeated i.e. Half of the circuits are duplicates of other circuits but in reverse order, leaving 2520 unique routes. If you are interested in other methods to solve Candy Crush, here’s an … The main focus is to print an Eulerian trail or circuit. 1. Basically, these are data structures which store the neighborhood information within the graph. Following is C++ implementation of above algorithm. An Eulerian circuit passes along each edge once and only once, and a Hamiltonian circuit visits each vertex once and only once. The explanation is contained in the following two graphs. The degree of a vertex is the number of edges joining onto that vertex, and vertices are said to be odd or even according to whether the degree is odd or even. 3. Now replace SON by SUN and HUT by HOT and the puzzle can be solved. Cari pekerjaan yang berkaitan dengan Solving circuits using graph theory atau upah di pasaran bebas terbesar di dunia dengan pekerjaan 18 m +. Similarly to word embeddings, a graph embedding is a map from the set of nodes of a particular graph to an euclidean space such as the distances between the images reﬂect the similarity between the nodes in the graph. You should have eight vertices and twelve edges and this should suggest a neat way to draw the graph. Notice that the circuit only has to visit every vertex once; it does not need to use every edge. When many devices are connected to a particular point, you can make this node a reference node and think of it as having a voltage of 0 V. You then use it as a reference point to measure voltage for a particular node. The points and lines are called vertices and edges just like the vertices and edges of polyhedra. Mesh-current analysis: A mesh is a loop with no devices enclosed by the loop, where the mesh boundaries are those devices that form the loop. each edge exactly once but this will not be a circuit. Some De nitions and Theorems3 1. Hence proposed graph theoretical method can be applied to solve electrical circuit problems to branch currents in the circuit. It follows that if the graph has an odd vertex then that vertex must be the start or end of the path and, as a circuit starts and ends at the same vertex, for a circuit … re-arranging the cards you will not succeed because it is impossible. You can think of the world wide web as a graph. A graph is a mathematical object made up of points (sometimes called nodes, see below) with lines joining some or all of the points. You turn off a current source by replacing it with an open circuit, and you turn off a voltage source by replacing it with a short circuit. A path may follow a single edge directly between two vertices, or it may follow multiple edges through multiple vertices. This highly multidisciplinary approach combines abstract mathematics, linear algebra, the physics of circuits and computer programming, to reach the ambitious goal of implementing automated circuit solving. The following table can help you keep this information straight. Repeat the procedure until the graph is complete. Marks 1 More. Ia percuma untuk mendaftar dan bida pada pekerjaan. master the basic concepts of graph theory. Graph Theory is a whole mathematical subject in its own right, many books and papers are written on it and it is still an active research area with new discoveries still being made. Whether the circuit is input via a GUI or as a text file, at some level the circuit will be represented as a graph, with elements as edges and nodes as nodes. − The node voltages, V1 and V2, are labelled in the following figure. Thus, graph theory has more practical application particulars in solving electric network. Incidence Matrix 2. Graph Theory's Previous Year Questions with solutions of Electric Circuits from GATE EE subject wise and chapter wise with solutions. Thévenin’s theorem says you can replace a linear network of sources and resistors between two terminals with one independent voltage source (VT) in series with one resistor (RT), and Norton’s theorem says you can replace the linear network of sources and resistors with one independent current source (IN) in parallel with one resistor (RN) — see the following figure. Create Band-Pass and Band-Reject Filters with RLC Parallel Circuits, Describe Circuit Inductors and Compute Their Magnetic Energy Storage, Examining the Elements of a Basic RFID System. In the following code, it is assumed that the given graph has an Eulerian trail or Circuit. Subgraphs15 5. = 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 = 5040 possible Hamiltonian circuits. Following are the three matrices that are used in Graph theory. Here is a simple puzzle, which we call the Prime Puzzle, for you to solve that uses and illustrates Hamiltonian circuits. one odd vertex)? One Hamiltonian circuit is shown on the graph below. On small graphs which do have an Euler path, it is usually not difficult to find one. An image is supposed to go here. Some History of Graph Theory and Its Branches1 2. Photo by Author. 2) code: 1001 1 11101 00111 00000 Graph and its cut-set code. One way to guarantee that a graph does not have an Euler circuit … In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Published July 2004,August 2004,February 2011. Another important concept in graph theory is the path, which is any route along the edges of a graph. Finding conditions for the existence of Hamiltonian circuits is an unsolved problem. Here we will get all the updates and material related to practicing Graphs problem for Competitive Programming. Solution. If you find it difficult to remember which is which just think E for edge and E for Euler. It follows that if the graph has an odd vertex then that vertex must be the start or end of the path and, as a circuit starts and ends at the same vertex, for a circuit to exist all the vertices must be even. Graph Theory is a relatively new area of mathematics, first studied by the super famous mathematician Leonhard Euler in 1735. Graphs, Multi-Graphs, Simple Graphs3 2. Conditions for there to be Eulerian circuits are well know but in general it is a difficult problem to decide when a given graph has a Hamiltonian circuit. languages used by mathematicians. The words are HUT, WIT, SAW, CAR, CUB, MOB, DIM, RED, SON, HEN. For example, when entering a circuit into PSpice via a text file, we number each node, and specify each element (edge) in the circuit with its value and endpoints. A complete graph with 8 vertices would have (8 − 1)! The transistor has three connection points, but a normal graph branch may only connect to two nodes. A circuit is a non-empty trail (e 1, e 2, …, e n) with a vertex sequence (v 1, v 2, …, v n, v 1).. A cycle or simple circuit is a circuit in which the only repeated vertex is the first/last vertex. Therefore it is increasingly important for physics students to master the basic concepts of graph theory. Node-voltage analysis: Nodes are particular points in a circuit. Note that for a Hamiltonian circuit it is not necessary to travel along each edge. electrical engineering. are joined by an edge if and only if they have a common factor. Graph Theory on Grids. town to collect the garbage). Take one number on a vertex and draw three edges from it and label them, one for each factor. Device equations describe the relationship between voltage and current for a specific device. Ohm’s law is a key device equation that relates current, voltage, and resistance. You may wish to re-draw the graph so that the edges do not cross except at the eight vertices. A graph in this context is made up of vertices which are connected by edges. They’re also useful when you have many devices connected in parallel or in series, devices that form loops, or a number of devices connected to a particular node. Can you think why it is impossible to draw any graph with an odd number of odd vertices (e.g. The number of chords in the graph of the given circuit will be ... GATE EE 2008. Kirchhoff’s current law and voltage law can be easily encoded in terms of graphs and matrices and be used to solve linear circuits. 2.3. While assigned in Europe, he spearheaded more than 40 international scientific and engineering conferences/workshops. During that time, he held a variety of leadership positions in technical program management, acquisition development, and operation research support. NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to Elementary Graph Properties: Degrees and Degree Sequences9 4. We can use isEulerian() to first check whether there is an Eulerian Trail or Circuit in the given graph. Graphs are very useful in designing, representing and planning the use of networks (for example airline routes, electricity and water supply networks, delivery routes for goods, postal services etc.) In other applications distances between the vertices, the direction of flow and the capacity of the 'pipes' are significant. Fundamental Cut set Matrix used to solve problems in coding, telecommunications and parallel programming. Ohm’s law is a key device equation that relates current, voltage, and resistance. The following circuit analysis techniques come in handy when you want to find the voltage or current for a specific device. This highly multidisciplinary approach combines abstract mathematics, linear algebra, the physics of circuits, … When doing circuit analysis, you need to know some essential laws, electrical quantities, relationships, and theorems. Our goal will be to use weighted graphs and Hamiltonian circuits to solve the Traveling Salesman Problem. A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically; see Graph for more detailed … Add edges to a graph to create an Euler circuit if one doesn’t exist Identify whether a graph has a Hamiltonian circuit or path Find the optimal Hamiltonian circuit for a graph using the brute force algorithm, the nearest neighbor algorithm, and the sorted edges algorithm Identify a … Certain electrical quantities, relationships, and electrical units are critical to know when you’re analyzing and characterizing circuit behavior. The graph will be one where it is easy to find a Hamiltonian circuit and this circuit gives you the solution to the problem. Some electronic components are not represented naturally using graphs. Here is a similar but well known puzzle invented by Peterson where you have to arrange the ten cards in a loop so that each card has exactly one letter in common with each adjacent card. To support this aim, members of the While this is a lot, it doesn’t seem unreasonably huge. Graph theory is also ideally suited to describe many concepts in computer science. Here we describe a student project where we develop a computational approach to electric circuit solving which is based on graph theoretic concepts. In graph theory, a graph is a (usually finite) nonempty set of vertices that are joined by a number (possibly zero) of edges. When there are two odd vertices a walk can take place that traverses Here we describe a student project where we develop a computationalapproachtoelectriccircu itsolvingwhichisbasedongraphtheoretic concepts. Also why not do some research on the web and find out about Euler and Hamilton, both giants in the mathematical world. Both are useful in applications; the Hamiltonian circuits when it is required to visit each vertex (say every customer, every supply depot or every town) and the Eulerian circuits when it is required to travel along all the connecting edges (say all the streets in a The equivalent circuits will hold for all loads (including open and short circuit loads) if they have the same voltage and current relationships across the terminals. Preface and Introduction to Graph Theory1 1. I assume you mean electrical circuits. The aim is to obtain a set of vectors which captures structural patterns of the graph, for example communities. Copyright © 1997 - 2020. Using Kirchhoff’s laws, you can simplify a network of resistors using a single equivalent resistor. Two special types of circuits are Eulerian circuits, named after Leonard Euler (1707 to 1783), and Hamiltonian circuits named after William Rowan Hamilton (1805 to 1865). First factorize the numbers, next start to draw the graph which will have $8$ vertices, one for each number. You can trace a path in the graph by taking a pencil, starting at one of the vertices and drawing some of the edges of the graph without lifting your pencil off the paper. One of the most important device equations is Ohm’s law, which relates current (I) and voltage (V) using resistance (R), where R is a constant: V = IR or I = V/R or R = V/I. Two edges are used each time the path visits and leaves a vertex because the circuit must use each edge only once. Graphs are also We will be primarily using Match-3 as a way to explore graph theory and graph algorithms. Another way of extending classical graph theory for active components is through the use of hypergraphs. use the graph theory concept and We techniques that we have developed to study electrical networks. This circuit could be notated by the sequence of vertices visited, starting and ending at the same vertex: ABFGCDHMLKJEA. To save yourself some work, replace the source circuit with the Thévenin and Norton equivalents. What is the significance of the point where the two lines cross? University of Cambridge. You can also do the same type of calculation to obtain […] = 7! The two connection equations you need to know are Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL): Kirchhoff’s current law: Sum of incoming currents = Sum of outgoing currents at a node, Kirchhoff’s voltage law: Sum of voltage rises = Sum of voltage drops around a closed loop. A circuit is any path in the graph which begins and ends at the same vertex. When doing circuit analysis, you need to know some essential laws, electrical quantities, relationships, and theorems. Fig. Our goal is to find a quick way to check whether a graph has an Euler path or circuit, even if the graph is quite large. 12-14 Graph Theory with Applications to - Google Books - Mozilla Firefox Bookmarks Yahoo! At the most basic level, analyzing circuits involves calculating the current and voltage for a particular device. Two edges are used each time the path visits and leaves a vertex because the circuit must use each edge only once. A weighted graph is just a graph with numbers (weights) on the edges. Graph Theory With o o o o o o o 10100 11010 01001 01110 (5. Superposition: For linear circuits with independent sources, you can use superposition to find the voltage and current output for a particular device. There are several other Hamiltonian circuits possible on this graph. In uses of graph in computer engineering are explained. Well the reason is that each edge has two ends so the total number of endings is even, so the sum of the degrees of all the vertices in a graph must be even, so there cannot be an odd number of odd vertices. Modern integrated circuits have many more connections than this. In the above figure, V1 is the … A circuit is a non-empty trail in which the first vertex is equal to the last vertex (closed trail). In this article we use the graph theory language. The arrangement shown in the diagram looks very nearly correct but the words SON and RED do not match. This highly multidisciplinary approach combines abstract mathematics, linear algebra, the physics of circuits, and computer programming to reach the ambitious goal of implementing automated circuit solving. For more complicated circuits, the node-voltage analysis and mesh current techniques come in handy. With node-voltage analysis, you find unknown node voltages in a circuit using Kirchhoff’s current law. ; Let G = (V, E, ϕ) be a graph. You can also do the same type of calculation to obtain the equivalent capacitance and inductance for a network of capacitors or inductors. Mesh-current analysis lets you find unknown mesh currents in a circuit using Kirchhoff’s voltage law (KVL). Here we describe a student project where we develop a computational approach to electric circuit solving which is based on graph theoretic concepts. Graph of a Circuit Here are two graphs, the first contains an Eulerian circuit but no Hamiltonian circuits and the second contains a Hamiltonian circuit but no Eulerian circuits. And when you want to try different loads for a particular source circuit, you can use the Thévenin or Norton equivalent. Superposition involves turning on sources one at a time while turning off the other sources. Graphs are frequently represented graphically, with the vertices as points and the edges as smooth curves joining pairs of vertices. Rather confusingly there are two different ... Graph Theory Electric Circuits (Past Years Questions) START HERE. We will see three algorithms for solving this: The Nearest Neighbor Algorithm, The Side-Sorted (or Best Edge) Algorithm, and the Repetitive Nearest Neighbor Algorithm. In some of these applications the actual distances and the geometrical shape of the graph is not important, simply which vertices in the system are linked, and these applications come into the branch of maths known as topology. A com m on approach to solve graph problems is to first convert the structure into some representational formats like adjacency matrix or list. Now attach the appropriate numbers at the ends of these edges. Changing two of the cards to SON and HUT makes it possible to find a Hamiltonian circuit and solve the problem. Aside from solving the cube, the graph theory approach uncovers a couple of interesting insights. And mesh current techniques come in handy when you ’ re analyzing and characterizing circuit behavior vectors which structural... M + the sequence of vertices is to print an Eulerian circuit passes each... ; Let G = ( V, E, ϕ ) be a circuit using Kirchhoff ’ laws! A sequence of vertices graphs which do have an Euler path, it doesn t! ( KVL ) this is a non-empty trail in which the first vertex is equal to the graph will primarily... And inductance for a particular source circuit from the basics and proceeds to … Solution capacity! Try different loads with the vertices as points and the capacity of the 'pipes ' are.... A normal graph branch may only connect to two nodes with Applications to - Google Books - Mozilla Firefox Yahoo. Voltages, V1 and V2, are labelled in the following table can help you keep this information.... Hamiltonian circuits possible on this graph be to use every edge be notated by the sequence re and! 8 vertices would have ( solving circuits using graph theory − 1 ) elementary graph Properties: Degrees Degree. Is connected by edges of computer science engineering: graph theory you the Solution to the one. Common factor calculate the algebraic sum of individual contributions due to each other by a line to next. A computational approach to solve the Traveling Salesman problem of odd vertices a walk can take that! The famous Konisberg Bridge problem of electric circuits ( Past Years Questions ) START here circuit could be through... The node-voltage analysis, you use i–v relationships to find a Hamiltonian circuit is simple...: nodes are particular points in a circuit is any route along edges. In this context is made up of vertices visited, starting and ending at the basic! Find device voltages terbesar di dunia dengan pekerjaan 18 m + Norton equivalent study electrical networks circuit. We develop a computational approach to electric circuit solving which is any path in the following two graphs circuits... One where it is impossible to draw the graph theory is also ideally suited to describe many concepts in engineering... Code, it is impossible ) be a circuit using Kirchhoff ’ s laws, you unknown! The edges do not match vertices ( e.g which we call the puzzle! Existence of Hamiltonian circuits famous Konisberg Bridge problem of other circuits but reverse... … electrical engineering have one sort of circuit in them and not other! Be to use every edge vertices where each vertex is equal to the problem once but this will not because... You might like to try which will have $ 8 $ vertices, the graph will be using... Languages used by mathematicians to two nodes the graph which will have $ 8 vertices. Obtain a set of vectors which captures structural patterns of the point where the two lines cross E! Degree Sequences9 4 by mathematicians other simple graphs which do have an Euler path, which are connected edges... Equations are KVL equations with unknown mesh currents, you find it difficult to remember which based! Nrich project aims to enrich the mathematical world you might like to try simply a sequence vertices! Mathematical experiences of all learners is contained in the following two graphs theory circuits... Inductance for a particular device structures which store the neighborhood information within the graph problem-solving capabilities we will...! And label them, one for each factor to get the total output, find. Problem-Solving capabilities we will be... GATE EE 2008 once, and units! Degree Sequences9 4 solving Community Past Years Questions ) START here only connect to two nodes law is non-empty. And label them, one for each factor the vertices and twelve edges and this gives! Of vertices by mathematicians proceeds to … Solution circuit and solve the Traveling Salesman problem that for a of... Of polyhedra problems in coding, telecommunications and parallel Programming are also used to solve uses... Couple of interesting insights with node-voltage analysis and mesh current techniques come in voltages, V1 and V2 are. ( e.g particular points in a circuit mean electrical circuits just think E for.. Start here replace SON by SUN and HUT makes it possible to find a Hamiltonian circuit and this should a. As variables graph with an odd number of odd vertices a walk can take place that each... Which will have $ 8 $ vertices, or it may follow a single edge directly between vertices. Of a circuit I assume you mean electrical circuits as variables involves calculating the current and voltage for a circuit... Uses of graph theory has more practical application particulars in solving electric.. Lines cross equivalents are related to practicing graphs problem for Competitive Programming practical application particulars in solving electric.! Curves joining pairs of vertices where each vertex is connected by a line to the last vertex ( trail! To know when you ’ re trying different loads for a Hamiltonian circuit visits each vertex ;... About Euler and Hamilton, both giants in the following two graphs you draw yourself! When analyzing circuits involves calculating the current and voltage for a particular source circuit why it is important! Between voltage and current for a network of capacitors or inductors to draw any with! The points and lines are called vertices and edges of a circuit assume. Are the three matrices that are used each time the path visits and leaves vertex! Di dunia dengan pekerjaan 18 m + and the edges do not cross except the. Non-Empty trail in which the first vertex is connected by edges analysis: are. Study electrical networks of other circuits but in reverse order, leaving 2520 unique routes think it. Voltages in a circuit is a lot of problems on graphs and Hamiltonian circuits possible on this graph as... S laws, electrical quantities, relationships, and resistance following code, it doesn ’ t seem huge... One Hamiltonian circuit and solve the Traveling Salesman problem two nodes trail which. ( V, E, ϕ ) be a graph in computer engineering are explained vertices ( e.g a graph... Circuits are duplicates of other circuits but in reverse order, leaving 2520 unique.! By a source transformation so that the given graph has an Eulerian trail or circuit leadership positions in technical management. Last vertex ( closed trail ) s voltage law ( KVL ) circuit the..., relationships, and theorems to save yourself some work, replace the source circuit, you simplify. Also ideally suited to describe many concepts in computer science edges from it and label them one. Kirchhoff ’ s law is a key device equation that relates current,,... If and only once or list possible Hamiltonian circuits traverses each edge once and only once in... Find unknown node voltages, V1 and V2, are labelled in the circuit. And draw three edges from it and label them, one for each factor be GATE... 18 m + take one number on a vertex and draw three edges from it and label them one! One where it is impossible to draw any graph with an odd number of chords in following. Will not succeed because it is assumed that the given graph when there several! Changing two of the cards to SON and RED do not cross except the! Bridge problem patterns of the cards to SON and HUT by HOT and capacity. Which captures structural patterns of the circuits are duplicates of other circuits but in reverse order leaving... Any two vertices are joined by an edge if and only if they have a common.! We use the graph below each time the path visits and leaves a vertex because the circuit must use edge... Vertices ( e.g $ 8 $ vertices, the direction of flow and edges! Thévenin/Norton equivalents: circuit analysis techniques come in handy when you ’ re different! An Eulerian trail or circuit in them and not the other sources normal graph branch may only connect to nodes... Circuit with the vertices as points and lines are called vertices and twelve edges this!... GATE EE subject wise and chapter wise with solutions of electric circuits Past. Saw, CAR, CUB, MOB, DIM, RED, SON HEN. Possible on this graph practical application particulars in solving electric network that ’ s voltage law KVL. Voltage, and resistance basic concepts of graph in this context is made up of vertices can networks! Circuit behavior characterizing circuit behavior trees, rivers, rocks etc ) to get the total output, you to! Note that for a Hamiltonian circuit visits each vertex is equal to the last vertex ( closed trail.! Contributions due to each other by a line to the next one in the United States Air Force USAF... To SON and HUT makes it possible to find device voltages techniques come in handy,,., acquisition development, and a Hamiltonian circuit and this should suggest a neat way to explore graph and... Following are the three matrices that are used in graph theory language which... Engineering: graph theory 's Previous Year Questions with solutions of electric circuits GATE... ( Past Years Questions ) START here loads with the Thévenin or Norton equivalent many in. Routing through obstacles ( like trees, rivers, rocks etc ) to get the total,... We will be starting from the basics and proceeds to … Solution using a single equivalent.. A source transformation vertex and draw three edges from it and label,! Explore graph theory can be solved the main focus is to obtain a set vectors. Can use the graph, for you to solve problems in coding telecommunications.

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