Prove that the graph below has no Hamilton circuit by pointing out a subset of vertices whose removal results in more connected components than vertices removed a b m n

Q: 2. Draw a directed graph which has the following adjacency matrix. Be sure to label the vertices and…

A: Draw the directed graph, using adjacency matrix

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

A: If G1 and G2 are isomorphic then they must have the same number of edges.But if G1 and G2 have same…

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

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Q: Find the edge chromatic number of Kn when n is positive integer.

A: We have to find the edge chromatic number of  when  is positive integer.

Q: Find: Euler circuit of K Hamilton path of W5. Trail of K5.

A: please see the next step for solution

Q: 2. Say that for any pair of people, they either both know each other, or they are strangers (neither…

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Q: 1.36. Show that if G is a tree then for any pair of vertices a, b there is exactly one path from a…

A: Given that, G be a tree. As, G be a tree that implies that, G is connected and G has no cycle. Since…

Q: Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. How…

A: Given : Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and…

Q: Prove that if there is a circuit in a graph that starts and ends at a vertex v and if w is another…

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Q: How many edges are in the graph with n nodes where every pair of nodes are joined by an edge? Prove…

A: Given To find the number of edges are in the graph with n nodes where every pair of nodes are joined…