2 3 5 F Figure 1: Graph Drawing A B E D Problem 3. Determine a) the number of isomorphisms between the two graphs in Figure 1. b) the number of automorphisms of each of these graphs. Screenshot

Determine if the following pairs of simple graphs are isomorphic. If they are, label the graph on the right to display the isomorphism. If they aren't, name a graph theoretic property that they don't share. (a) (b) (c) (d)

show graph (on A and C) manually

4. (a) Let T be a tree with 50 edges. The removal of certain edge from T yields two disjoint trees T1 and T2. Given that the number of vertices in T1 equals the number of edges in T2, determine the number of vertices and the number of edges in T1 and T2.Also, show that a regular binary tree has an odd number of vertices. (b) Define isomorphism between graphs? Check whether the following two graphs are isomorphic or not. Justify your answer.