On the unitary Cayley graphs of matrix algebras

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.