Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Vaidyanathan Sivaraman

Committee Member

Robert C. Smith

Committee Member

Paul Fabel

Committee Member

Mohammad Sephrirar

Date of Degree

8-6-2021

Original embargo terms

Worldwide

Document Type

Graduate Thesis - Open Access

Major

Mathematics

Degree Name

Master of Science

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

Both chordal and weakly chordal graphs have been topics of research in graph theory for many years. Upon reading their definitions it is clear that the weakly chordal class of graphs is a relaxation of the chordal condition for graphs. The question is then asked could we possibly find and study the properties if we, in turn, relaxed the weakly chordal condition for graphs? We start by providing the definitions and basic results needed later on. In the second chapter, we discuss perfect graphs, some of their properties, and some subclasses that were researched. The third chapter is focused on a new class of graphs, the definition of which relaxes the restrictions for chordal and weakly chordal graphs, and extends certain results from weakly chordal graphs to this class.

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