Show that in a simple graph with at least Two vertices there must be two vertices that have the same degree.

Q: Does this have 12 vertices? If not, how does that change the drawing and answers?

A: IntroductionGraph: A graph is a visual representation of edges and vertices, or dots and lines.A…

Q: In a simple graph there can two edges connecting two vertices. True O False

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Q: Sketch an undirected graph with the following vertex degrees 3,3,3,2,1 if it exists

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Q: If a simple disconnected graph has 7 vertices and 2 connected components what is the maximum number…

A: Given question is If a simple disconnected graph has 7 vertices and 2 connected components what is…

Q: A 4-partite graph is bipartite. True or False

A: False

Q: Define a pseudo graph?

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Q: Show that in every simple graph there is a path from every vertex of odd degree to some other vertex…

A: we have to prove that In every simple graph there is a path from every vertex of odd degree to some…

Q: Among each pair of the CEOs of N companies there is (a) mutual like; (b) mutual dislike; (c) neutral…

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Q: Show that if a simple graph G ha

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

Q: Can a graph with nine vertices and nine edges exist? Explain wy no such graph exists or draw the…

A: To verify whether a graph with 9 vertices  & 9 edges exist or not.

Q: If G1 is a simple graph with 20 edges and G has 25 edges, how many vertices does G1 have?

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Q: How can one prove a graph is connected?

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Q: Show that every simple finite graph has two vertices of the same degree.

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Q: Could there be a graph with four vertices of degree 1,2,5 and 4? Explain why no such graph exists or…

A: To verify whether a graph with 4 vertices of degree 1,2,5 and 4 exist or not.

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: Draw all nonisomorphic simple graphs with four vertices and no more than two edges.

A: Given: The objective is to draw all the nonisomorphic simple graphs with the four vertices and no…

Q: Can a simple graph exist with 9 vertices all of degree 5?

A: Handshaking lemma: In any graph, sum of degree of all the vertices is twice the number of edges…

Q: Complete a path straight at vertex a that ends at vertex c.

A: A complete path is defined when all the vertices are passed through and none of the smaller paths…

Q: Let P₁ and P₂ be two paths of maximum length in a connected graph G. Prove that P₁ and P2 have a…

A: To prove that two paths P1 ​ and P2 ​ of maximum length in a connected graph GGG have a common…