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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