Part A: How many non-isomorphic loop-free graphs with 7 vertices and 5 edges are possible? [N0 multi- graphs] [Notez provide a picture of the graphs that you came up with. Check your graphs carefully to make sure that no two are isomorphic. Part B: Give an example of a graph G with 8 vertices which contains no subgraph isomorphic to K 3 , and, contains no subgraph isomorphic to I: . (Just one graph that has both properties. Draw the graph and submit a picture of it.) Part C: Let a graph G = (V, E) be defined as follows: Let S = {a, b, c, d, e, f}. Let V be the set of all 3- element subsets of S. Two vertices are adjacent if and only if they share exactly two elements in common. For example the vertex {a, b, c} is adjacent to the vertex {a, b, d}. However, {a, b, c} is not adjacent to {a, d, e}. a) How many vertices are in G? b) What is the degree of each vertex? c) How many edges are in G