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