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- 6. Find the complement of the graph K3,2, the complete bipartite graph on (3, 2) vertices.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 edges3. Generalize Sanjay determined that one vertex of a figure was mapped to its image by translating the point 2 units left and 7 units down. What is the rule that maps the other vertices of the figure to their images?Q. No. 6 (a) For the graph shown below (4) (1) find number of edges (ii) find number of vertices (ii) find number of loops; (iv) find number of parallel edges; (b) which following graphs are bipartite. Explain with reason. (4)
- How many edges are in the graph with n nodes where every pair of nodes are joined by an edge? Prove your answer.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.B\ Prove that " there is no simple graph on four vertices, three of whic have degree 3 and the remaining vertex has degree 1".
