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Beijing Jiaotong University

Time: 16:00-18:00 (GMT+8), Monday November 21st, 2022

Location: Tencent Meeting

**Abstract:**
A Cayley (di)graph \(\mathrm{Cay}(G,S)\) of a group \(G\) with respect to a subset \(S\) of \(G\) is called *normal* if the right regular representation of \(G\) is a normal subgroup in the full automorphism group of \(\mathrm{Cay}(G,S)\), and is called a *CI-(di)graph* if for every \(T\subseteq G\), \(\mathrm{Cay}(G,S)\cong \mathrm{Cay}(G,T)\) implies that there is \(\sigma\in \mathrm{Aut}(G)\) such that \(S^\sigma=T\).
We call a group \(G\) an *NDCI-group* if all normal Cayley digraphs of \(G\) are CI-digraphs, and an *NCI-group* if all normal Cayley graphs of \(G\) are CI-graphs, respectively. In this paper, we prove that a cyclic group of order \(n\) is an NDCI-group if and only if \(8\nmid n,\) and is an NCI-group if and only if either \(n=8\) or \(8\nmid n\).

Host: 谢贻林 Yilin Xie