DM-Graphs-Q8

+1 vote

A represents an adjacency matrix of Graph G

                                                   \begin{bmatrix} 0& 1&0&0\\ 1 & 0 & 1 & 1\\ 0 & 1 & 0 & 0\\ 0 & 1 & 0 & 0 \end{bmatrix}

The number of paths of length 8  from vertex 1 to vertex 4.

asked Jul 12 in Discrete Maths by gbeditor (16,060 points)
reshown Jul 13 by gbeditor

1 Answer

0 votes

 

 

Answer is 0   (I am not sure plz suggest)

answered Jul 13 by tssoumambanerjee-nit (1,040 points)
find A^8 matrix and entry (1,4) in A^8 is required answer.
answer should be 27 A^8 have to computed by taking adjacent matrix
Is there any shortcut to find the same? or do we need to calculate by multiplying it 8 times
how is A^8 soln of this question?
A^8 could be calculated by cayley hamilton theorem ,but not getting an idea why A^8 is soln of this question
In matrix a^n each (i,j) entry gives the no of paths of length n from i to j.
Answer:
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