On the unitary Cayley graphs of matrix algebras

We study a family of Cayley graphs on the group of n×n matrices Mn(F), where F is a finite field and n is a natural number, with the connection set of GLn(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 Mn(F) is either invertible or sum of two invertible matrices. Moreover, we show that GMn(F) is class 1 if and only if charF=2. Finally, it is shown that for each graph G and each finite field F, G is an induced subgraph of Cay(Mn(F),GLn(F)).