On the Enumeration of Certain Weighted Graphs
Abstract
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 $\frac{p(x)}{(1x)^{m+1}}$, where $m$ is the number of vertices of the graph and $p(x)$ is a polynomial of degree at most $m$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606163
 Bibcode:
 2006math......6163B
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 25 pages