A FAMILY OF ARC-TRANSITIVE GRAPHS OF GIRTH AT LEAST 5 ADMITTING A SUZUKI SIMPLE GROUP

Georgy A. Glinskikh     (Ural Federal University, 51 Lenina Str., Yekaterinburg, 620000, Russian Federation)
Ludmila Yu. Tsiovkina     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108, Russian Federation)

Abstract


We give a construction of a new family of Deza graphs of girth at least 5 that possess an arc-transitive group of automorphisms isomorphic to a Suzuki simple group \(Sz(q)\). To study their combinatorical properties, we elaborate some group-theoretic arguments involving classical results on the groups of given type.




Keywords


Arc-transitive graph, Suzuki group, Graph of girth at least 5, Triangle-Free Graph, Deza graph

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References


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DOI: http://dx.doi.org/10.15826/umj.2025.2.008

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