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- 4. Is the graph below bipartite? If so, list the vertices in the one part and the vertices in the second part. As in left = { list of vertices} and right = { list of vertices}How long can a path be in the complete bipartite graph k(m,n)?QUESTION 11 Total number of edges of a complete graph which has 9 vertices is None 18 edges 12 edges 36 edges
- How many edges are in the graph with n nodes where every pair of nodes are joined by an edge? Prove your answer.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 edge between x E A and y E B if and only if x + y is a multiple of 3. What is the size of N({2})? What is the size of N({2,5})? What is the size of N({2,6})? Is there a matching in this graph?12b) Identify if each of the following graphs is bipartite or not bipartite. 3 ii)
- 4. Prove: " Show that the number of edges in a simple planar graph of order n is at most 3n – 6". Give an example and explanation to validate the proof.Among each pair of the CEOs of N companies there is (a) mutual like; (b) mutual dislike; (c) neutral feeling. A trade delegation of the maximum size needs to be formed such that it does not have any pair of members with mutual dislike. Transform this problem to a graph theoretic problem. What are the vertices of the graph? What are the edges of the graph? What do you have to find in the graph?Let G be a simple graph with exactly 11 vertices. Prove that G or its complement G must benon-planar. Hint: The maximum number of edges in a planar graph with n vertices is 3n − 6.Please write in complete sentences, include all details, showall of your work, and clarify all of your reasoning.
