On the δ-conjecture for graphs with minimum degree |G| – 4

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.

Grantor dc:publisher

University of Tennessee at Chattanooga

Author dc:creator

• Villanueva, Matthew

Contributors dc:contributor

• Barioli, Francesco
• Van der Merwe, Lucas; Ledoan, Andrew; Kuhn, Stephen
• College of Arts and Sciences

• Graph theory
• Mathematical analysis
• Matrices
• Algebras, Linear

Licence

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

Language dc:language

English, eng

Repository record dc:identifier

https://scholar.utc.edu/theses/507

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-1656