Finding Patterns in the Inertia of the Distance Squared Matrix of Unicyclic Graphs

Author

Kellon Sandall, Brigham Young UniversityFollow
Mark Kempton, Brigham Young UniversityFollow
Christian Howell, Brigham Young UniversityFollow

Author Date

2022-06-09

Degree Name

BS

Department

Mathematics

College

Physical and Mathematical Sciences

Defense Date

2022-06-01

Publication Date

2022-06-09

First Faculty Advisor

Mark Kempton

First Faculty Reader

Benjamin Webb

Honors Coordinator

Michael Griffin

Keywords

inertia, unicyclic, cycle, graph, tree

Abstract

We analyze the spectrum of the distance squared matrix of a tree and give a relation between the inertia of the distance squared matrix and the structure of the tree. We take the result one step further and consider the addition of exactly one cycle in the tree. We obtain an expression for the inertia of the distance squared matrix of a cycle graph. We obtain a bound on the inertia of the distance squared matrix of an arbitrary unicyclic graph.

BYU ScholarsArchive Citation

Sandall, Kellon; Kempton, Mark; and Howell, Christian, "Finding Patterns in the Inertia of the Distance Squared Matrix of Unicyclic Graphs" (2022). Undergraduate Honors Theses. 254.
https://scholarsarchive.byu.edu/studentpub_uht/254

Handle

http://hdl.lib.byu.edu/1877/uht0250