(a) Consider the simple graph G1 which has the vertex set V1 = {1,2,3,4,5,6} and which has the following adjacency matrix, with respect to the natural ordering of the vertices: 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 OO 1 0 1 1 1 0 1 (0) Draw a diagram that illustrates the graph G1. You are given the following information about three simple graphs H1,H2,H3. For each of the following three statements, identify which graphs are definitely not isomorphic to G1 and which graphs might be isomorphic to G1. Provide an explanation for each decision you make - marks are awarded only for answers that contain an explanation. The size of Hy is six. H2 has exactly five vertices that have the same degree value. The vertices of Hz are labelled using letters. Consider the directed graph G2 as shown: (b) 2 3 4 | Let M be the adjacency matrix of graph G2, with respect to the natural ordering of the vertices. (a) Write down M. (b) By inspection of the graph G2, or otherwise, evaluate the first row of M}