Date of Graduation
Eberly College of Arts and Sciences
John L Goldwasser
Michael E Mays
James D Mooney
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.
Tichenor, Todd, "Topics in Graph Compositions" (2015). Graduate Theses, Dissertations, and Problem Reports. 6811.