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Arezoomand, Majid, Taeri, Bijan. (1394). A classification of finite groups with integral bi-Cayley graphs. , 4(4), 55-61. doi: 10.22108/toc.2015.7807
Majid Arezoomand; Bijan Taeri. "A classification of finite groups with integral bi-Cayley graphs". , 4, 4, 1394, 55-61. doi: 10.22108/toc.2015.7807
Arezoomand, Majid, Taeri, Bijan. (1394). 'A classification of finite groups with integral bi-Cayley graphs', , 4(4), pp. 55-61. doi: 10.22108/toc.2015.7807
Arezoomand, Majid, Taeri, Bijan. A classification of finite groups with integral bi-Cayley graphs. , 1394; 4(4): 55-61. doi: 10.22108/toc.2015.7807

A classification of finite groups with integral bi-Cayley graphs

Transactions on Combinatorics
مقاله 42، دوره 4، شماره 4، اسفند 2015، صفحه 55-61    اصل مقاله (221.86 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2015.7807
نویسندگان
Majid Arezoomand* 1؛ Bijan Taeri2
1Departmant of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran
2Department of Mathematics, Isfahan University of Technology, Isfahan, Iran
چکیده
The bi-Cayley graph of a finite group $G$ with respect to a subset $S\subseteq G$‎, ‎which is denoted by $BCay(G,S)$‎, ‎is the graph with‎ ‎vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1)‎, ‎(sx,2)\}\mid x\in G‎, ‎\ s\in S\}$‎. ‎A‎ ‎finite group $G$ is called a \textit{bi-Cayley integral group} if for any subset $S$ of‎ ‎$G$‎, ‎$BCay(G,S)$ is a graph with integer eigenvalues‎. ‎In this paper we prove‎ ‎that a finite group $G$ is a bi-Cayley integral group if and only if $G$ is isomorphic to‎ ‎one of the groups $\Bbb Z_2^k$‎, ‎for some $k$‎, ‎$\Bbb Z_3$ or $S_3$‎.
کلیدواژه‌ها
bi-Cayley graph؛ Integer Eigenvalues؛ Representations of finite groups
مراجع
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