Cubic Graphical Regular Representations of PSU₃(q)

2022/01/12 by Li, Jing Jian, Xia, Binzhou, Zhang, Xiao Qian +1
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2201.04307

Abstract

A graphical regular representation (GRR) of a group G is a Cayley graph of G whose full automorphism group is equal to the right regular permutation representation of G. Towards a proof of the conjecture that only finitely many finite simple groups have no cubic GRR, this paper shows that PSU₃(q) has a cubic GRR if and only if q≥4. Moreover, a cubic GRR of PSU₃(q) is constructed for each of these q.

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