Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Sivaraman, Vaidyanathan

Committee Member

Dang, Hai

Committee Member

Smith, Robert

Committee Member

Yarahmadian, Shantia

Committee Member

Sepehrifar, Mohammad

Date of Degree

12-8-2023

Document Type

Dissertation - Open Access

Major

Mathematical Sciences

Degree Name

Doctor of Philosophy (Ph.D)

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

A graph in which every edge is labeled positive or negative is called a signed graph. We determine the number of ways to sign the edges of the McGee graph with exactly two negative edges up to switching isomorphism. We characterize signed graphs that are both sign-symmetric and have a frustration index of 1. We prove some results about which signed graphs on complete multipartite graphs have frustration indices 2 and 3. In the final part, we derive the relationship between the frustration index and the number of parts in a sign-symmetric signed graph on complete multipartite graphs.

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