Todd Tichenor

Date of Graduation

2015

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Mathematics

Committee Chair

Michael Mays

Committee Co-Chair

Marjorie Darrah

Committee Member

Harvey Diamond

Committee Member

John L Goldwasser

Committee Member

Michael E Mays

Committee Member

James D Mooney

Abstract

For any discrete undirected graph G with vertex set V(G) and edge set E(G) (respectively), a graph composition of G is defined to be a partition of V(G) where every element of the partition yields a connected, induced subgraph of G. This dissertation is comprised of 5 chapters. The first is a general introduction to the concept of graph compositions and a survey of previously researched work; the second focuses on the composition number of deletions of specific graphs from complete graphs; the third focuses on establishing bounds for the composition number of general graphs and the Bell number coefficients of general graphs; the fourth focuses on the connection between graph compositions and Aitken's array, a well researched array; finally, the fifth focuses on the number of compositions of graphs where the number of components is restricted.

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