#### Title of Presentation or Performance

A Look at Multi-Decompositions of Complete Graphs into Graph Pairs of Order 4

#### Type of Submission (Archival)

Event

#### Expected Graduation Date

2016

#### Location

Atrium, Center for Natural Sciences, Illinois Wesleyan University

#### Start Date

4-20-2013 2:00 PM

#### End Date

4-20-2013 3:00 PM

#### Disciplines

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 ofgraph theory, graph decomposition is an active field of research. One type of decomposition is graph pairs. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studieddecompositions of complete graphs into graph-pairs of order four. In their proof, they left a small part to the readers. We will complete this proof.

#### Included in

A Look at Multi-Decompositions of Complete Graphs into Graph Pairs of Order 4

Atrium, 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 ofgraph theory, graph decomposition is an active field of research. One type of decomposition is graph pairs. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studieddecompositions of complete graphs into graph-pairs of order four. In their proof, they left a small part to the readers. We will complete this proof.