Transitive regular $q$-analogs of graphs
Dean Crnkovic, Vedrana Mikulic Crnkovic, Andrea Svob, Matea Zubovic, Zutolija
TL;DR
This paper develops a method for constructing transitive regular $q$-analogs of graphs, extending the theory of $q$-analogs of designs and graphs, and provides concrete examples including $q$-analogs of quasi-strongly regular graphs.
Contribution
It introduces a novel construction method for transitive regular $q$-analogs of graphs and explores their properties with new examples, including $q$-analogs of quasi-strongly regular graphs.
Findings
Constructed new transitive regular $q$-analogs of graphs.
Provided examples of $q$-analogs of quasi-strongly regular graphs.
Extended the theory of $q$-analogs in combinatorics.
Abstract
In 1976, Delsarte introduced the notion of -analogs of designs, and -analogs of graphs were introduced recently by M. Braun et al. In this paper, we extend that study by giving a method for constructing transitive regular -analogs of graphs. Further, we illustrate the method by giving some examples. Additionally, we introduced the notion of -analogs of quasi-strongly regular graphs and give examples of transitive -analogs of quasi-strongly regular graphs coming from spreads.
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Taxonomy
TopicsRings, Modules, and Algebras · Graph theory and applications · Finite Group Theory Research