Bell Numbers of Graphs.

摘要

Let G be a simple graph with vertex set V( G). Let F be a family of graphs such that K1 ∈ F . Denote by B(G; F ) the number of unordered partitions of V( G) such that each part induces a member of F . We call B(G; F ) the Bell number of the graph G with respect to the family F . We investigate properties of this function for different families F , and conditions on F for the function B(G; F ) to have certain properties.