Suppose G is a simple connected graph such that G is unicyclic. Prove that |V (G)| = |E(G)|.  Please explain in details with steps included for me to understand.

Q: Determine whether the given pair of graphs are isomorphic. Exhibit an isomorphism or provide a…

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Q: Determine (with proof) whether or not G1 and G2 (drawn below) are isomorphic. and determine (with…

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Q: Prove that if G is a graph with no isolated vertices, then α'(G) +β'(G) = n(G)

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Q: In graphing, prove that at least one of G and it's complement, G', is connected.

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Q: Prove that having n vertices, where n is a positive integer, is an invariant for graph isomorphism.

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Q: (d) Show that the pair of graphs are not isomorphic by showing that there is a property that is…

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Q: When n = 3, there are nonisomorphic simple graphs.

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Q: For the graphs shown below, either exhibit an isomorphism between vertex sets or explain why the…

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Q: The following graphs are isomorphic Select one: True O False

A: The graph are given above in the question.

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Q: Determine if the following pairs of simple graphs are isomorphic. If they are, label the graph on…

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Q: Use Kuratowski's theorem to prove that the following graph is not planar.

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Q: Verify the Handshaking theorem of the following graphs

A: To verify : The Handshaking theorem for the following graphs: (a) (b)

Q: 11. Are the following graphs isomorphic? Explain how you know. U2 V2 V5 V3 V4

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Q: В. С. D. А.

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Q: Prove that every graph G on {1,... n} which is acyclic and has n 2 edges has exactly 2 connected…

A: Given: To prove the given statement as follows:

Q: Prove that the graphs in the figure below are isomorphic: (2 6. a

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Q: Prove that the two graphs below are isomorphic.

A: Graph G and H are isomorphic if there exists an isomorphism between them.

Q: True/False: If the graphs G1 and G2 are isomorphic, and G, is connected, then G2 must be connected…

A: If G1 and G2 are isomorphic , and G1 is connected

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

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Q: 3 5

A: Isomorphism of graph: Let G and H be two graphs. They are said to be isomorphic if there exists a…

Q: . Determine whether the given pair of graphs is isomorphic. Exhibit an isomorphism or provide a…

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Q: Suppose a graph G has 22 vertices. What is the minimum number of EDGES that G must contain if Diracs…

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Q: If G has at least one vertex of degree greater than zero then there are two of even degree as long…

A: This is the problem of graph theory.

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Q: Are the ff. two graphs isomorphic? 一 一 一 1. 1. 1. 1. -

A: To find Are the ff. Two graphs isomorphic.

Q: Draw all subgraphs of this graph

A: Given: There are 3 vertices, hence there will be 23=8 sub graphs Graph nodes: Nodes is defined as…

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Q: The graph given below can described as Choose as many that applies. A planar B complete cyclic…

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Q: Provide an easy-to-understand explanation for the direct proof problem below: For every graph that…

A: Given, for every graph that is undirected (no self-loops or multi-edges) with n nodes.

Q: . Determine if the following graphs are isomorphic or not? If yes, show how are they isomorphic. If…

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Q: Draw a complete graph so that it has symmetry with respect to the origin. (0,0) (x,0) -2t -2-

A: Topic = Graphs Correct option = C

Q: Suppose G is a simple undirected graph with n vertices. If G is self-complementary, prove that…

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Q: Give an example of a non-planar graph that is not contractible to K5or K3,3.

A: Solution :-

Q: Are the following two graphs isomorphic? If yes, define the isomorphism between the two graphs. If…

A: the number of vertices in first graph = 5 the number of edges in first graph = 5 degree of vertices…

Q: Give an example of two undirected graphs G1 with nodes {f, s, y, r} and G2 with nodes {t, q, n, p,…

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Q: Show all possible connected sub graphs of the following graph. How many of them are there refer to…

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Q: Let G be a simple graph with 20 vertices. Suppose that G h ponents, and every pair of distinct…

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Q: Prove that if G is a graph of order p and has size greater than ¹) then G is connected. 2

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Q: Show that the Petersen graph is nonplanar. [Hint: show that the graph is edge contractible to Ks).

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: 36. и

A: In figure 1.  Degree of the vertex are :  deg(u1)=3, deg(u2)=2 ,deg(u3)=3 , deg(u4)=3 , deg(u5)=3…

Q: What is a(G) if G is a complete graph on n vertices?

A: It is given that G is a complete graph on n vertices. Also provided are some basic definitions about…