Defense Date

2022

Document Type

Thesis

Degree Name

Master of Science

Department

Mathematical Sciences

First Advisor

Craig Larson

Abstract

A diameter-2-critical (D2C) graph is a graph with diameter two such that removing any edge increases the diameter or disconnects the graph. In this paper, we look at other lesser-studied properties of D2C graphs, focusing mainly on their independence number and minimum degree. We show that there exist D2C graphs with minimum degree strictly larger than their independence number, and that this gap can be arbitrarily large. We also exhibit D2C graphs with maximum number of common neighbors strictly greater than their independence number, and that this gap can be arbitrarily large. Furthermore, we exhibit a D2C graph whose number of distinct degrees in its degree sequence is strictly greater than its independence number. Additionally, we characterize D2C graphs with independence number 2 and show that all such graphs have independence number greater or equal to their minimum degree.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

5-13-2022

Share

COinS