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 graph shown below is Eulerian or Not * Eulerian   Not Eulerian

determine whether

Draw every simple graph with five vertices and four edges (isolated vertices are allowed) up to isomorphism (if two graphs are isomorphic, just draw one of them).

Show that the pair of graphs are not isomorphic by showing that there is a property that is preserved under isomorphism which one graph has and the other does not. Figure 5: Two undirected graphs. The first graph has 5 vertices, in the form of a regular pentagon. From the top vertex, moving clockwise, the vertices are labeled: 1, 2, 3, 4, and 5. Undirected edges, line segments, are between the following vertices: 1 and 2; 2 and 3; 3 and 4; 4 and 5; and 5 and 1. The second graph has 4 vertices, a through d. Vertices d and c are horizontally inline, where vertex d is to the left of vertex c. Vertex a is above and between vertices d and c. vertex b is to the right and below vertex a, but above the other two vertices. Undirected edges, line segments, are between the following vertices: a and b; b and c; a and d; d and c; d and b.

How can one prove a graph is connected?