Let G be a graph with vertices (1,2,...,n) and adjacency matrix A= (a subtext ij)
1) Find an expression for the number of walks of the form i-k-j.
I'm puzzled. I thought I had it figured out as:
entry in ik + entry in kj -1
but this did not hold when I looked at graphs with multiple loops. Any thoughts?
Here is another that I can't even figure out where to begin with.
2) Show that the number of walks of length 2 from vertex i to vertex j in G is the ijth entry of the matrix A^2.
I know how to multiply matrices, but I'm not sure how to put it in general terms to help me.