$q$-Analogs of strongly regular graphs
Michael Braun, Dean Crnkovi\'c, Maarten De Boeck, Vedrana, Mikuli\'c Crnkovi\'c, Andrea \v{S}vob
TL;DR
This paper introduces q-analogs of strongly regular graphs, explores their properties, and establishes connections to finite field designs, providing a classification and necessary parameter conditions.
Contribution
It is the first to define q-analogs of strongly regular graphs and analyze their properties and classifications.
Findings
Established a necessary condition on parameters
Connected q-analogs to designs over finite fields
Provided examples and a classification of these structures
Abstract
We introduce the notion of q-analogs of strongly regular graphs and give several examples of such structures. We prove a necessary condition on the parameters, show the connection to designs over finite fields, and present a classification.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Rings, Modules, and Algebras