Domination in transformation graph G(-+-)

Let G= (V,E) be a simple undirected graph of order n and size m. The transformation graph of G is a simple graph with vertex set V(G), E(G) in which adjacency is defined as follows: (a) two elements in V(G) are adjacent if and only if they are non-adjacent in G (b) two elements in E(G) are adjacent if and only if they are adjacent in G and (c) one element in V(G) and one element in E(G) are adjacent if and only if they are non-incident in G. It is denoted by G(-+-). In this paper, we investigate the domination number of transformation graph. We prove that gamma(G (broken vertical bar) )<= 3 and characterise the graphs for which this number is 1, 2 or 3.