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- W4300942324 abstract "A finite group $G$ admits an {em oriented regular representation} if there exists a Cayley digraph of $G$ such that it has no digons and its automorphism group is isomorphic to $G$. Let $m$ be a positive integer. In this paper, we extend the notion of oriented regular representations to oriented $m$-semiregular representations using $m$-Cayley digraphs. Given a finite group $G$, an {em $m$-Cayley digraph} of $G$ is a digraph that has a group of automorphisms isomorphic to $G$ acting semiregularly on the vertex set with $m$ orbits. We say that a finite group $G$ admits an {em oriented $m$-semiregular representation} if there exists a regular $m$-Cayley digraph of $G$ such that it has no digons and $G$ is isomorphic to its automorphism group. In this paper, we classify finite groups admitting an oriented $m$-semiregular representation for each positive integer $m$." @default.
- W4300942324 created "2022-10-04" @default.
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- W4300942324 date "2022-08-08" @default.
- W4300942324 modified "2023-10-14" @default.
- W4300942324 title "On oriented $m$-semiregular representations of finite groups" @default.
- W4300942324 doi "https://doi.org/10.48550/arxiv.2208.03912" @default.
- W4300942324 hasPublicationYear "2022" @default.
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