1. The following graph is called Petersen graph, it is named after Danish mathematician Julius Petersen. Answer the following questions related to Petersen graph. a) Represent Petersen graph with adjacency list and adjacency matrix. b) How many edges are there in Petersen graph? c) Is Petersen graph bipartite? Why? d) Show that Petersen graph is not planar. (Read Example 9 on Page 725.) e) Show that the vertex connectivity of Petersen graph is at most 3. f) Show a vertex cut in Petersen graph of size 3. g) Show an edge cut in Petersen graph of size 3. h) Does Petersen graph contain any Eulerian trail? Why? d i) Show a Hamiltonian path in Petersen graph. j) Show a 3-coloring in Petersen graph.

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Q: 3. Find the tree and tree cover of Petersen graph. ***** *****

A: The Petersen Graph

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Q: Total number of edges of a complete graph which has 9 vertices is None 12 edges 36 edges 18 edges

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Q: 4. Prove that the following is another drawing of the Petersen graph.

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Q: 10) Add one edge to the graph in order to get a regular graph of degree 3.

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Q: 1. Suppose G is a planar graph with four faces of lengths 3, 4, 5, 6. How many edges are there in G?

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Q: Show that the following is another drawing of the Petersen graph: 4

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Q: 1. Does there exist a disconnected graph of order 10 having 36 edges? Explain.

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