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.
2 comments:
Interesting! Sadly, at the moment I only understand the first solution. Hopefully (or not) after going through some graph theory subject(s) I'll understand it better.
Interesting, anyway :)
Excellent observation. Couldn't notice that while watching the movie.
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