On the unitary Cayley graphs of matrix algebras

被引：10
|
作者：
Kiani, Dariush [1 ,2 ]
Mollahajiaghaei, Mohsen [3 ]
机构：
[1] Amirkabir Univ Technol, Dept Math & Comp Sci, Tehran 15914, Iran
[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran
[3] Univ Western Ontario, Dept Math, London, ON N6A 5B7, Canada
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 466卷
关键词：
Unitary Cayley graph; Strongly regular; Edge regular; Matrices; REPRESENTATIONS;
D O I：
10.1016/j.laa.2014.10.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a family of Cayley graphs on the group of n x n matrices M-n(F), where F is a finite field and n is a natural number, with the connection set of GL(n)(F). We find that this graph is strongly regular only when n = 2. We find diameter of this graph and we show that, every matrix in M-n(F) is either invertible or sum of two invertible matrices. Moreover, we show that G(Mn)(F) is class 1 if and only if char F = 2. Finally, it is shown that for each graph G and each finite field F, G is an induced subgraph of Cay(M-n(F), GL(n)(F)). (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：421 / 428
页数：8
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