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

页码：421 / 428

页数：8

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