# 群与图讨论班 Seminars on Groups and Graphs

You are here: Seminars > 2022 > November 21st

# On CI-property of normal circulant digraphs

## 谢金华 Jinhua Xie

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

Slides