Find the number of paths of length 'n' between any two vertices in K4 if the value of n is 4,5.
(The problem belongs to Discrete Mathematics by Kenneth H Rosen, Sect 8.4 , problem no. 17)
when the value of n is 2 or 3, it can be solved by observation.
Is there a general formulae for the purpose ?
Thanks in advance
If you want to find the general answer, then see if you can diagonalize the adjacency matrix. Then you can easily take arbitrary powers of the matrix.