Automorphisms and domination numbers of transformation graphs over vector spaces

Let F-q be a finite field of q elements, V-0 an n-dimensional vector space over F-q and T-0 the set of all linear transformations of V-0. Let V = V-0 \ {0} and let T be the subset of T-0 consisting of all irreversible nonzero linear transformations on V-0. The transformation graph of V-0, written as Gamma(V), is a bipartite graph, whose vertex set V is partitioned into two colouring sets as V = T boolean OR V and there is an undirected edge between A is an element of T and v is an element of V if and only if A maps v to the zero vector, that is A(v) = 0. In this paper, the domination number and the automorphisms of Gamma(V) are determined.