Given an adjacency matrix A = [ [0, 1, 1], [1, 0, 1], [1, 1, 0] ], The total no. of ways in which every vertex can walk to itself using 2 edges is ________?Group of answer choices6248
Question
Given an adjacency matrix A = [ [0, 1, 1], [1, 0, 1], [1, 1, 0] ], The total no. of ways in which every vertex can walk to itself using 2 edges is ________?Group of answer choices6248
Solution
The adjacency matrix A represents a graph with 3 vertices. The number of ways in which every vertex can walk to itself using 2 edges can be found by squaring the adjacency matrix.
The square of the adjacency matrix A is calculated as follows:
A^2 = [ [0, 1, 1], [1, 0, 1], [1, 1, 0] ] * [ [0, 1, 1], [1, 0, 1], [1, 1, 0] ]
= [ [2, 1, 1], [1, 2, 1], [1, 1, 2] ]
The diagonal elements of the resulting matrix represent the number of ways each vertex can walk to itself using 2 edges.
So, the total number of ways in which every vertex can walk to itself using 2 edges is 2 + 2 + 2 = 6.
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