Consider the network shown in the image. A double headed arrow i-j indicates that there is an edge i → j and an edge j→i. Compute the number of paths in this network consisting of exactly 5 edges, which start'at the vertex 1 and end at the vertex 2. 1 5 2 4 3

Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: Given; There 10 points in a plane such that no three points are collinear

Q: 2.) Determine how many backtracks are required to use every edge at least once returning to where…

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Q: Each node can have at most n=v number of edges. (True means Doğru; False means Yanlış) Birini seçin:…

A: Result: 1. The maximum number of edges in an undirected graph is n(n-1)/2. 2. The maximum number of…

Q: How many edges does Ks have? Kn in general?

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Q: find the minimum Hamilton circuit from the table starting at G. 10 10 12

A: Given The given table is Nearest Neighbor Algorithm→ i) Pick a starting vertex. ii) select the…

Q: Let x and y be two adjacent vertices in the complete bipartite graph Kn,n,     n ≥ 3. Find the…

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Q: Consider a complete network formed by 7 nodes. Does this network have an Eulerian сycle? OYes ONo…

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Q: 4. Solve the travelling problem for the given graph by finding the total weight of all Hamilton…

A: A Hamilton circuit is a cycle which contain paths such that each path visit each vertex exactly…

Q: Does a Hamiltonian path or circuit exist on the graph below?

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Q: 2. Apply Euler's Theorems and Fleury's Algorithm to determine Euler path and Euler circuits in each…

A: Given:

Q: you are to Concidernee Knm is the Complete bi- Partite graph on A, B where A hasn elements oul B has…

A: Given the complete bipartite graph Kn,m on A and B where A has n elements and B has m elements. A…

Q: Suppose that the edges of Kn are weighted-- what is the largest number of edges that cou be in the…

A: We will use the method of combinatorics to answer this question.

Q: 4. Solve the travelling problem for the given graph by finding the total weight of all Hamilton…

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Q: Show that the average degree of a vertex in the triangulation is strictly less than 6.

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Q: The directed line segment whose initial point is the origin is in ________ ________.

A: Our Aim is to tell what the directed line segment is being called whose initial point is the origin.

Q: Define the following: i. Euler tour ii. Hamilton path

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Q: 2. From the set of relation {(1,1), (1,2), (1,4), (2,1), (2,2), (2,4), (3,3), (4,3), (4,4)}, draw…

A: As per our guideline we are allowed to answer only one question. Kindly submit the other question as…

Q: The set of North-East lattice paths start from (0,0), end at (n-k, n+k), and they do not go below…

A: Given below clear explanation

Q: 4. Solve the travelling problem for the given graph by finding the total weight of all Hamilton…

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Q: 9. Obtain the shortest distance and shortest path from vertex 1 to every other vertex in the network…

A: To find the shortest distance between the vertex 1 to every other vertex .

Q: ee with m edges has m-1 vertices True

A: We are asked find whether the statement is true or false

Q: WHAT is this type of circuit or graph a. Hamiltonian circuit b.Euler path c.Hamiltonian path d.Euler…

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Q: Prove or disprove (by giving a counterexample) that a graph G with n 2 4 vertices and ("5') +3 edges…

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Q: 3. Recall that Km,n denotes a complete bipartite graph on (m, n) vertices. a. Draw K4,2- b. Draw…

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Q: If countries in the Southeast region are consisting of archipelagos then other foreign countries…

A: Euler diagram is a general diagram giving meaningful information about things that are related to…

Q: 3. Determine the classification of the quadrilateral: Vertices are (0,0), (5,2), (10,10), & (0,6)…

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Q: 10 What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5, 1) that…

A: Use mid section formula for evaluating the coordinates of points.

Q: 4. Solve the travelling problem for the given graph by finding the total weight of all Hamilton…

A:

Q: Consider a bipartite graph on the set A = {1,2,3,4,5,6} and B = {7,8,9,10,11,12}, where there is an…

A: Given: A bipartite graph is defined on set A={1,2,3,4,5,6} and    B={7,8,9,10,11,12}. Here there is…

Q: (d) State Euler's Theorem on Eulerian circuits in multigraphs. (e) Use Euler's Theorem to decide if…

A: 4-(d) Euler's Theorem on Eulerian circuits in multigraphs. A graph has an Eulerian circuit if the…

Q: 8) Consider the directed graph below 1 point Ps P1 P2 PA The number of 2-step connections for this…

A: The adjacency matrix is given by A = 0010100010010100000101000 Then  A2 = 0010100010010100000101000…

Q: 1. Prove that in a finite directed graph if every edge has at least one outgoing edge, then the…

A: 1. It is given that the graph is directed and finite.Therefore it has finite vertex and it is given…

Q: 2 3

A: For a vertex x, the pair a,b under consideration are such that  i) a≠x,b≠x and  ii) there is a…

Q: 10 What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5, 1) that…

A: We have to find out coordinates

Q: Let G be a directed graph with 10 vertices. Let a and b be vertices that are connected by at least…

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Q: Let S be a u,v-walk in a graph G. Show that a shortest (in number of edges) u,v-walk contained in W…

A: It is given that S be a u,v walk in a graph G.

Q: Complete a circuit starting at vertex s that passes through vertex u

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Q: Consider the following networks (i) (ii) 5 1. 4 2. For each network determine: 4 а) а path b) а…

A: Hello, thanks for your question but according to our policy I am answering the first three subparts…

Q: Draw the multigraph G whose adjacency matrix is (0 1 2 0 1 1 1 1 A = 2 1 0 \o 1 0 Show that the…

A: Adjacency matrix We will see this with the example. For the given graph the adjacency matrix is as…

Q: 2. The following table represents a network with the arcs identified by their starting and ending…

A: Given that From the given data

Q: 3. Provide a graph (aside from the examples in our class discussion) that has an Eulerian path.…

A: Solution:

Q: 11) Consider the network below. Formulate an LP to find the shortest-route path from node 1 to node…

A: Given: The network flow

Q: (g) How many paths of length n exist between vertices 1 and 2 in the graph with adjacency matrix A?

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Q: Consider the following transshipment network for finding the shortest route from node 1 to node 7. 5…

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Q: Which of the following graphs have Euler circuits or Euler path? G F E K D R K A: Has Euler trail.…

A: Definition:- Let G is connected graph then (a) G contain Euler trail if and only if G contain…

Q: 13. Rectangle MNOP with vertices M(-2, 6), N(2, 8), O(5, 2), and P(1, 0): y = -x M' ( L N'L O'L P'LJ

A: Given data: M(-2,6) N(2,8) O(5,2) P(1,0) y=-x

Q: An Euler circuit of the graph K, is w K1 a (z, y, x, W, z, S, W) (V, z, x, W, z, s) (V, Z, X, W, z,…

A: Graph theory

Q: a. Let V = {x, y, z, u, v}. How many distinct graphs are there on the vertex set V with exactly 6…

A: We have given graph V{x,y,w,u,z} We need to calculate a)graph having 6 edges. b) The trail which is…