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.

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