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September 3rd, 2013, 09:08 PM  #1 
Newbie Joined: Aug 2013 Posts: 2 Thanks: 0  Combinations to navigate a noncyclic 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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combinations, directed, graph, navigate, noncyclic 
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