2022/08/09 by Jia‐Li Du, Du, Jia-Li, Young Soo Kwon +3 · 2 citations
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2208.04483
openalex publication_date 2022/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a group G, an \em m-Cayley digraph \G over G is a digraph that has a group of automorphisms isomorphic to G acting semiregularly on the vertex set with m orbits. We say that G admits an \em oriented m-semiregular representation (OmSR for short), if there exists a regular m-Cayley digraph \G over G such that \G is oriented and its automorphism group is isomorphic to G. In particular, O1SR is also named as ORR. Verret and Xia gave a classification of finite simple groups admitting an ORR of valency two in [Ars Math. Contemp. 22 (2022), #P1.07]. Let m≥ 2 be an integer. In this paper, we show that all finite groups generated by at most two elements admit an OmSR of valency two except four groups of small orders. Consequently, a classification of finite simple groups admitting an OmSR of valency two is obtained.