A new construction of Deza graphs through $\pi$-local fusion graphs of finite simple groups of Lie-type of even characteristic

TL;DR

This paper explores the structure of $$-local fusion graphs of certain finite simple groups of Lie-type with even characteristic, revealing their connection to Deza graphs and identifying infinite families of such graphs that are strictly Deza graphs.

Contribution

It introduces a new construction method for Deza graphs via $$-local fusion graphs of finite simple Lie-type groups of even characteristic, establishing their combinatorial significance.

Findings

Identifies strong connections between fusion graphs and combinatorial objects

Finds infinite families of $$-local fusion graphs that are strictly Deza graphs

Provides new insights into the structure of Deza graphs from group-theoretic constructions

Abstract

In this paper, we investigate the structure of $\pi$-local fusion graphs of some finite simple groups of Lie-type of even characteristic. We indicate a strong connection between such graphs and other combinatorial objects, as antipodal covers and Deza graphs. In particular, we find several infinite families of $\pi$-local fusion graphs of finite simple groups of Lie-type of even characteristic that are strictly Deza graphs.