Binomial Identities Generated by Counting Spanning Trees

We partition the set of spanning trees contained in the complete graph Kn into spanning trees contained in the complete bipartite graph Ks,t. This relation will show that any property of spanning trees in Kn can be derived from trees in Ks,t. We enumerate the trees in Kn and Ks,t recursively, and after applying the inclusion/exclusion principle of counting, we obtain some combinatorial and numerical identities. Among them are identities for np , where n and p are integers. Keywords. Cayley’s Theorem, spanning trees, binomial identities

• Type: Journal
• Year: 2007
• Where: ARSCOM
• Authors: Thomas Dale Porter
• Keywords: ARSCOM 2007, Complete Bipartite Graph, Complete Graph Kn, Identities