Generalized m series in tree enumeration.

Abstract

Consideration of a particular series formed by deleting certain branches of the complete graph K sub t with t vertices. A class of graphs which contains the m series as a special case is considered, and a new formula is given for the m series itself (an m series graph is obtained from K sub t by removing m branches forming a closed loop). A formula is derived for the number of labeled spanning trees in the graph obtained by deleting certain branches from K sub t.