For the the graph G(V,E) shown above, find the following :
- The matrix giving the number of 3 step walks in G : [Ak]ij is the number of paths of length k from i to j. So, the answer is A3.
- The generating function for walks from point i to j : The generating function is as follows. Here are more examples of generating functions.
- The generating function for walks from points 1 to 3 : Simplify the above formula using cramer's rule for i=1 and j=3.