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- 1. Let G(V, E) be an unweighted undirected graph. Its corresponding adjacency matrix is A, where a_ij = 1 if (i,j) is an edge and zero otherwise. The diagonals are all marked as 1. We multiply A by itself n times, n Solution a)every v i is connected with v i+1 and v i-1 .then we get regular graph..we can represent this graph using adjacency matrix we get normal square matrix . b)complete graph means every vertex is connected with other vertices..i.e,no self loops a ij=0 where i=j,and 1 if i not equal to j if we represent this type of graph using adjacency matrix we get all diagonal elments as 0(zero) when all diagonal elments are zero then that matrix we called it as hollow matrix c)graph where every vertex has zero degree means it is a null graph.. if we represent this null graph using adjacency matrix we get all zeros.so,it is zero matrix