On the Enumeration of Certain Weighted Graphs

Details On the Enumeration of Certain Weighted Graphs On the Enumeration of Certain Weighted Graphs

2006-06-07

arxiv.org/abs/math/0606163v1

Mathematics

Combinatorics

25 pages

Scientific paper

We enumerate weighted graphs with a certain upper bound condition. We also compute the generating function of the numbers of these graphs, and prove that it is a rational function. In particular, we show that if the given graph is a bipartite graph, then its generating function is of the form $\frac{p(x)}{(1-x)^{m+1}}$, where $m$ is the number of vertices of the graph and $p(x)$ is a polynomial of degree at most $m$.

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