Date of Award
12-2023
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
Committee Chair/Advisor
Dr. Wayne Goddard
Committee Member
Dr. Beth Novick
Committee Member
Dr. Matthew Macauley
Abstract
Several measures of vulnerability of a graph look at how easy it is to disrupt the network by removing/disabling vertices. As graph-theoretical parameters, they treat all vertices alike: each vertex is equally important. For example, the integrity parameter considers the number of vertices removed and the maximum number of vertices in a component that remains. We consider the generalization of these measures of vulnerability to weighted vertices in order to better model real-world applications. In particular, we investigate bounds on the weighted versions of connectivity and integrity, when polynomial algorithms for computation exist, and other characteristics of the generalized measures.
Recommended Citation
VanLandingham, Julia, "Generalized Vulnerability Measures of Graphs" (2023). All Theses. 4206.
https://tigerprints.clemson.edu/all_theses/4206