Suppose we are given a directed graph with n vertices, and let M be the n×n adjacency matrix corresponding to .a. Let the product of M with itself (M2) be defined, for 1 ≤ i, j ≤ n, as follows:where “⊕” is the boolean or operator and “⊙” is boolean and. Given this definition, what does M2(i, j) = 1 imply about the vertices i and j? What if M2(i, j) = 0?b. Suppose M4 is the product of M2 with itself. What do the entries of M4 signify? How about the entries of M5 = (M4)(M)? In general, what information is contained in the matrix Mp?c. Now suppose that is weighted and assume the following:If M2(i, j) = k, what may we conclude about the relationship between vertices i and j?
Suppose we are given a directed graph with n vertices, and let M be the n×n adjacency matrix…
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