This Is AuburnElectronic Theses and Dissertations

Bell Numbers of Graphs

Date

2012-05-04

Author

Duncan, Bryce

Type of Degree

dissertation

Department

Mathematics and Statistics

Abstract

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.