Given the adjacency matrix of an undirected grapha b ca 2 1 3b 1 1 1c 3 1 0How many paths of length 3 are there from the vertex b to the vertex a in this graph?Select one:a.27b.21c.None of thesed.33e.18
Question
Given the adjacency matrix of an undirected grapha b ca 2 1 3b 1 1 1c 3 1 0How many paths of length 3 are there from the vertex b to the vertex a in this graph?Select one:a.27b.21c.None of thesed.33e.18
Solution
To find the number of paths of length 3 from vertex b to vertex a, we need to raise the adjacency matrix to the power of 3 and then look at the entry in the 2nd row and 1st column (since we are looking for paths from b to a).
The adjacency matrix is:
2 1 3
1 1 1
3 1 0
Raising this matrix to the power of 3 gives us:
46 18 12
18 6 6
12 6 10
So, there are 18 paths of length 3 from vertex b to vertex a. Therefore, the answer is e.18.
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