If G1 and G2 are isomorphic, must they have the same number of edges? If G1 and G2 have the same number of edges must they be isomorphic? If not, give an example.

Q: If G1 and G2 are isomorphic, must they have the same number of vertices? If G1 and G2 have the same…

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Q: 4. Let G = (V, E) be a graph with vertex-set V = {1, 2, 3, 4, 5, 6} and edge-set = = {(1, 2), (3,…

A: Graph theory. Draw the graph, maximum and minimum degree of the graph

Q: Discrete Math-Graph Theory) Let G=(V,E₁∪E₂) be a simple graph such that G₁=(V,E₁) and G₂=(V,E₂) are…

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Q: 4. Prove: "Show that the number of edges in a simple planar graph of order n is at most 3n – 6".…

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Q: 7. Prove that the complete bipartite graph Km,n is the join of the complements of Km and kn.

A: To prove that the complete bipartite graph is the join of the complements of and , we need to show…

Q: 29. Let G be a graph with vertex set VG and edge set Ec. Let V C VG and EC EG. Is there always a…

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Q: A trail is a walk that does not repeat an edge. Prove that a trail that repeats a vertex must…

A: Assume that vertex Vk is repeated Let the trail be W: V1V2.....Vk........Vn....Vi.....Vk.......Vj…

Q: When two graphs G and H are isomorphic, this means: there exists a bijection between the vertices of…

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Q: When two graphs G and H are isomorphic, this means: there exists a bijection between the vertices of…

A: Two graphs G and H are said to be isomorphic, if there exist a bijection f between their vertices…

Q: Prove that the following two graphs are isomorphic using properties of incidence and adjacency…

A: The star graph with the labels is as follows: The adjacency matrix of the star graph is as follows:…

Q: Graphs G and H are said to be isomorphic if the vertices are in one-to-one correspondence and the…

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Q: Prove that connecting two nodes u and v in a graph G by a new edge creates a new cycle if and only…

A: Given, Connecting two nodes u and v in a graph G by a new edge creates a new cycle such that if and…

Q: . Let G be a graph with V = {1,2, 3, 4, 5, 6} and no edge between an odd and even vertex (a) Draw…

A: Given that V={1,2,3,4,5,6} a) draw the graph G with the maximum number of edges b) How many…

Q: b 8 b) Explain (in words) how you could find the number of paths between vertex a and vertex e which…

A: As per the question we are given a undirected graph with seven vertices a, b, c, d, e, f, g And we…

Q: Draw a directed graph consisting of five nodes, each of which is path connected to every other node…

A: please see the next step for solution

Q: Show that if a simple graph G has n vertices and at least n edges, then G must contain a cycle.

A: We have to Show that if a simple graph G has n vertices and at least n edges, then G must contain a…

Q: "If G has a walk that uses all the edges, then G is connected." I know that this statement is false…

A: If G has a walk that uses all the edges, then G is connected Clearly this statement is false For…

Q: Prove or disprove that if G has m edges and n vertices, then the degeneracy of G is at least m

A: Given  be a graph with m edges and n vertices. Required to prove that the degeneracy of G is at…

Q: 9. Which edges could be re-used in order to find an optimal Eulerization of the following graph? (1)…

A: The objective is find which edges that could be re-used to find the optimal Eulerization of the…

Q: What are the strongly connected components of the digraph below? Your answer should consist of a…

A: A graph is said to be strongly connected if every vertex is reachable from every other vertex. The…

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A: To find- Which of the following relations represented by the directed graph is symmetric?   Concept…

Q: what is a complete fuzzy graph And give examples

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Q: A theoretical framework involves the identification of network of relationships among variables…

A: Answer: True.

Q: The graph G is a planar connected graph. It has 22 edges, and 15 vertices. How many faces does G…

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Q: What are the edges incident on v2? (b) What are the vertices adjacent to v2 ? (c) What are the…

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Q: Indicate two edges such that after deleting these two edges the resulting graph is bipartite. Then…

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Q: Let G be a graph with 10 vertice and 5 components. If a vertex is removed from G, the number of…

A: Answer: 9 and 4

Q: 9. Suppose two graphs G and H have the same vertex set V. (a) Provide an example where deg, (v) =…

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Q: 2.5 Prove that if a graph has exactly two vertices of odd degree, then there is a path from one of…

A: In graph theory, a graph consists of vertices and edges.The degree of a vertex is the number of…

Q: If G is a Hamiltonian graph, then G has no cut-vertex. True or false? Justify

A: In order to find the solution of the given question, we will use the concept of Hamiltonian graph…

Q: 2.29. Is this graph planar (the edges cross each other in the middle but there is no vertex there)?

A: Planar graph: When a connected graph can be drawn without any edges crossing it is called planar.…

Q: (b) I had a go, and could see the following partial representation (b, A₁), (c, A2) and (d, A3).…

A: As per the question, we are given a partial representation consisting of three pairs, (b, A1), (c,…

Q: Which of the following statement/s is/are true or false? * Statement I: With Hamilton cycle, every…

A: Hamilton cycle is a closed path which visits every vertex exactly once. So some edge may not be used…

Q: The Euler's formula v - e + f = 2 holds for all connected planar graphs. What if the graph is not…

A: The formula for multiple connected component c is, v +f = e + c + 1

Q: Consider the network with N = 4 nodes and adjacency matrix A given by A = 0 11 1 1 0 1 1 0000 0000

A: Approach to solving the question:(e) PageRank Centrality and Calculation for Each Node Definition of…

Q: (2х - 1)" Σ Which of the following statements are false for the power series ? n- n=1 I: Series is…

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