Senior Honors Projects, 2020-current
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
ORCID
https://orcid.org/0009-0009-2241-7337
Date of Graduation
12-13-2025
Semester of Graduation
Fall
Publish
yes
Degree Name
Bachelor of Science (BS)
Department
Department of Mathematics and Statistics
First Advisor
Joshua Ducey
Abstract
If Γ is a graph for which every edge is in exactly one clique of order ω, then one can form a new graph with vertex set equal to these cliques. This is a generalization of the line graph of Γ. We discover many general results and classifications related to these clique graphs that will be useful to researchers studying graphs with this property. In particular, we find bounds on the spectrum of Γ (with exact results when Γ is k-regular) and some complete classifications when Γ is strongly regular. We apply our results to derive novel information about the existence questions of certain strongly regular graphs. We also examine the critical group of graphs with this property and their associated transformations. Finally, we discuss examples of widely studied families of graphs that have this property, and provide some examples to make the results more concrete.
