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Zbl 0887.05025
Xu, Mingyao
Automorphism groups and isomorphisms of Cayley digraphs. (English)
[J] Discrete Math. 182, No.1-3, 309-319 (1998). ISSN 0012-365X

Let $G$ be a finite group and $S$ a subset of $G$, not containing the identity element 1. The Cayley digraph $X=\text{Cay} (G,S)$ is defined by $V(X)=G$ and $E(X)=\{(g,sg)\ |\ g\in G,\ s\in S\}$. A subset $S$ of $G$ is called a CI-subset of $G$, if for any subset $T$ of $G$ with $\text{Cay} (G,S)$ isomorphic to $\text{Cay} (G,T)$, there exists $\alpha \in\Aut(G)$ such that $S^\alpha=T$. A number of results on Cayley digraphs is obtained, for example, Proposition 3.5: Let $G$ be a finite group and $p$ the least divisor of $|G|$. Let $S$ be a generating set of $G$ with $|S|<p$. Then $S$ is a CI-subset.
[A.A.Makhnev (Ekaterinburg)]

MSC 2000:: *05C25 Graphs and groups
05C20 Directed graphs (digraphs)
20B25 Finite automorphism groups of miscellaneous structures

Keywords: Cayley digraph,; CI-subset of group

Cited in: Zbl 1078.05039 Zbl 0890.05032

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