Domination in transformation graph G – +–

Abstract

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 γ (G – + –) ≤ 3 and characterise the graphs for which this number is 1, 2 or 3.