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.
Recommended Citation
Gamladdalage, Kanchana Madhumali Gamlath Esweda, "On Independent Bondage Number and Total Bondage Number of Graphs" (2024). Electronic Theses and Dissertations. 2932.
https://egrove.olemiss.edu/etd/2932