On \BCI-groups and \CI-groups

2020/03/14 by Asieh Sattari, Sattari, Asieh, Majid Arezoomand +3 · 1 citation
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2003.06624

openalex publication_date 2020/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group and S be a subset of G. A bi-Cayley graph \BCay(G,S) is a simple and an undirected graph with vertex-set G×\1,2\ and edge-set \\(g,1),(sg,2)\| g∈ G, s∈ S\. A bi-Cayley graph \BCay(G,S) is called a \BCI-graph if for any bi-Cayley graph \BCay(G,T), whenever \BCay(G,S)≅\BCay(G,T) we have T=gS^σ for some g∈ G and σ∈\Aut(G). A group G is called a \BCI-group if every bi-Cayley graph of G is a \BCI-graph. In this paper, we showed that every \BCI-group is a \CI-group, which gives a positive answer to a conjecture proposed by Arezoomand and Taeri in \citearezoomand1. Also we proved that there is no any non-Abelian 4-\BCI-simple group. In addition all \BCI-groups of order 2p, p a prime, are characterized.

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• Normal Cayley digraphs of cyclic groups with CI-property

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