#### Title of Presentation or Performance

#### Type of Submission (Archival)

Event

#### Expected Graduation Date

2016

#### Location

Center for Natural Sciences, Illinois Wesleyan University

#### Start Date

4-12-2014 9:00 AM

#### End Date

4-12-2014 10:00 AM

#### Disciplines

Applied Mathematics

#### Abstract

Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate two vertices with each edge. Also, a decomposition of a graph is a list of subgraphs such that each edge appears in exactly one subgraph in the list. In the field of graph theory, graph decomposition is an active field of research. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studied decompositions of complete graphs into graph-pairs of order four and five. We are extending their results by investigating which complete graphs decompose into a specific graph pair of order 6.

#### Included in

Decomposing Complete Graphs into a Graph Pair of Order 6

Center for Natural Sciences, Illinois Wesleyan University

Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate two vertices with each edge. Also, a decomposition of a graph is a list of subgraphs such that each edge appears in exactly one subgraph in the list. In the field of graph theory, graph decomposition is an active field of research. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studied decompositions of complete graphs into graph-pairs of order four and five. We are extending their results by investigating which complete graphs decompose into a specific graph pair of order 6.