Title of Abstract

The Coprime Graph of Groups

Submitting Student(s)

Alan Way, Winthrop UniversityFollow

College

College of Arts and Sciences

Department

Department of Mathematics

Abstract

Recently, investigation of the coprime graph of a group was initiated. The coprime graph of a group is a graph with vertices as group elements and an edge between two vertices if and only if their order (in the group) is relatively prime. We will explore chromatic, clique, and independence number for certain classes of finite groups. In addition, we classify which abelian groups give rise to perfect coprime graphs. We obtain a partial result on the class of nonabelian groups.

Honors Thesis Committee

Jessica Hamm, Ph.D.; Arran Hamm, Ph.D.; and Kristen Abernathy, Ph.D.

Start Date

20-4-2018 1:30 PM

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Apr 20th, 1:30 PM

The Coprime Graph of Groups

West 221

Recently, investigation of the coprime graph of a group was initiated. The coprime graph of a group is a graph with vertices as group elements and an edge between two vertices if and only if their order (in the group) is relatively prime. We will explore chromatic, clique, and independence number for certain classes of finite groups. In addition, we classify which abelian groups give rise to perfect coprime graphs. We obtain a partial result on the class of nonabelian groups.