. (6 points) Let A be the adjacency matrix for a directed graph G on vertex...

 

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. (6 points) Let A be the adjacency matrix for a directed graph G on vertex set {1,2,3,4}. The first few powers of A are given below. 0 1 10 1 0 0 0 01 10 A = 1 0 0 0 1000 0 1 10 A - A 1 01 10 0 0 0 1000 A4= 1 0 0 0 01 10 01 10 0 1 1 0 1000 0 010 1 0 0 0 a) For what k is (2,3) in Gk? Explain your answer. b) How many closed walks of length 2 are in G? Explain your answer. . (6 points) Let A be the adjacency matrix for a directed graph G on vertex set {1,2,3,4}. The first few powers of A are given below. 0 1 10 1 0 0 0 01 10 A = 1 0 0 0 1000 0 1 10 A - A 1 01 10 0 0 0 1000 A4= 1 0 0 0 01 10 01 10 0 1 1 0 1000 0 010 1 0 0 0 a) For what k is (2,3) in Gk? Explain your answer. b) How many closed walks of length 2 are in G? Explain your answer.

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a To find for what k the vertex pair 23 is in Gk we need to analyze the powers of the adjacency matr... View the full answer