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September 3rd, 2013, 09:08 PM   #1
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Combinations to navigate a non-cyclic directed graph

Hello,

I need a formula and way (algorithm) to find all possibilities to navigate in a graph, with the following characteristics:
- The graph will have n number of nodes;
- The graph is directed (arrows);
- The graph is not cyclic, that is, the edges tend always to the next nodes;
- There are m types of edges, where m>=1;
- An edge 1 can reach the next node, an edge 2 achieves the second subsequent node (the next is jumping), and so on;
- Note that the last node will only receive nodes, and the latest will have restrictions on the number of edges because there are no more distant nodes;

I made a figure (half ugly I know) to help in understanding. It has nodes n = 12, m = 3 edges; black=1, red=2, blue = 3.
I need to know all the ways to navigate the graph, for example, the sequence of edges would these possibilities (and many others of course):
11111111111
1111111112
1211111111
121111121
2113211
33212

Note that the sum of the edges always give n - 1 (do not know if this helps)

I need a formal explanation, is for my dissertation.

I thank you!

Sorry my bad english, im brazilian.
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