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## Bell Numbers of Graphs

##### Date

2012-05-04##### Author

Duncan, Bryce

##### Type of Degree

dissertation##### Department

Mathematics and Statistics##### Metadata

Show full item record##### 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.