Committee Chair

Barioli, Francesco

Committee Member

Van der Merwe, Lucas; Ledoan, Andrew; Kuhn, Stephen

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

For a graph G of order n, the minimum rank of G is defined to be the minimum rank among all n × n symmetric matrices whose ij-entry is nonzero precisely when {i, j} is an edge of G. The delta conjecture proposes a relationship between the minimum rank and the minimum degree of a given graph. We prove that the delta conjecture holds for several classes of graphs; in particular, we show this relationship holds for many graphs G whose minimum degree is |G| – 4. We then consider some implications of these results related to other problems involving minimum rank.

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

5-2017

Subject

Graph theory; Mathematical analysis; Matrices; Algebras, Linear

Keyword

Minimum rank; Delta conjecture; Orthogonal representations; Graph; Graph complement

Document Type

Masters theses

DCMI Type

Text

Extent

ix, 56 leaves

Language

English

Rights

https://rightsstatements.org/page/InC/1.0/?language=en

License

http://creativecommons.org/licenses/by-nc-nd/3.0/

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