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.
Recommended Citation
Tichenor, Todd, "Topics in Graph Compositions" (2015). Graduate Theses, Dissertations, and Problem Reports. 6811.
https://researchrepository.wvu.edu/etd/6811
