Electronic Theses and Dissertations

Date of Award

1-1-2024

Document Type

Dissertation

Degree Name

Ph.D. in Mathematics

First Advisor

Bing Wei

Second Advisor

Talmage James Reid

Third Advisor

Haidong Wu

School

University of Mississippi

Relational Format

dissertation/thesis

Abstract

In this dissertation, we study the independent bondage number and total bondage number of some classes of graphs. We improve existing upper bounds for the independent bondage number of planar graphs with a minimum degree of 3 by expanding on the structural properties of planar graphs studied by Borodin and Ivanova [4] and Pham and Wei [19] using the discharging method. Additionally, we explore upper bounds for the independent bondage number under various girth conditions. Furthermore, we improve existing upper bounds for the total bondage number of trees and find upper bounds for the total bondage number of planar graphs with certain degree conditions. Moreover, we establish an upper bound for the total bondage number for a graph having a path with two 2-vertices at a distance of at most 3, as well as for complete multipartite graphs.

Available for download on Sunday, November 22, 2026

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