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Bell Numbers of Complete Multipartite Graphs

Authors: Julian Allagan, Christopher Serkan
Keywords: Bell number, Bell polynomial, Partition, Stirling numbers.

Abstract

The {\it Stirling number} $S(G;k)$ is the number of partitions of the vertices of a graph $G$ into $k$ nonempty independent sets and the number of all partitions of $G$ is its {\it Bell number}, $B(G)$. We find $S(G;k)$ and $B(G)$ when $G$ is any complete multipartite graph, giving the upper bounds of these parameters for any graph.

Julian Allagan
University of North Georgia
Watkinsville, Georgia, U.S.A
E-mail:

Christopher Serkan
University of North Georgia
Watkinsville, Georgia, U.S.A
E-mail: