Suppose we are given a directed graph G with n vertices, and let M be the n n adjacency matrix corresponding to G. (a) Let the produet of M with itself (M2) be defined, for 1 sijS n, as follows: where e is the logical oroperator and is the logical and operator. Given this definition what does M"(i, j) = 1 imply about the vertices i and j? what if M2(i))-07 (c) Now suppose that G is weighted and assume the following . for 1 . for 1 n, M(i, j) = weight(i,j) if (i, je E S i, j : n, M(i, j) = oo if (i, j) Also let Mr6.3) be defined, for 1 s i,jS n, as follows: M"(i, j) = min[M(i, 11+ M(1, j), , M(i, n) + M(n)]. If M2(i, j) = k, what may we conclude about the relationship between vertices i and j