@article {
author = {Arezoomand, Majid and Taeri, Bijan},
title = {Finite BCI-groups are solvable},
journal = {International Journal of Group Theory},
volume = {5},
number = {2},
pages = {1-6},
year = {2016},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2016.7265},
abstract = {Let $S$ be a subset of a finite group $G$. The bi-Cayley graph $BCay(G,S)$ of $G$ with respect to $S$ is an undirected graph with vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1),(sx,2)\}\mid x\in G, \ s\in S\}$. A bi-Cayley graph $BCay(G,S)$ is called a BCI-graph if for any bi-Cayley graph $BCay(G,T)$, whenever $BCay(G,S)\cong BCay(G,T)$ we have $T=gS^\alpha$ for some $g\in G$ and $\alpha\in Aut(G)$. A group $G$ is called a BCI-group if every bi-Cayley graph of $G$ is a BCI-graph. In this paper, we prove that every BCI-group is solvable.},
keywords = {Bi-Cayley graph,graph isomorphism,solvable group},
url = {https://ijgt.ui.ac.ir/article_7265.html},
eprint = {https://ijgt.ui.ac.ir/article_7265_5d7f9ab8bf8b6c396bfac5b1e7a5f461.pdf}
}