A Note on Incidence graphs

An incidence graph of a given graph G, denoted by I(G), has its vertex set V ( I ( G ) ) = { ( v e ) : v ∈ V ( G ) , e ∈ E ( G )   and   v   is incident to   e   in   G } such that the pair ( u e ) ( v f ) of vertices ( u e ) , ( v f ) ∈ V ( I ( G ) ) is an edge of I(G) if and only if there exists at least one case of u = v , e = f , u v = e or u v = f . Study of Incidence graphs was made by Zhagn Zhong-fu et al. in [Zhagn Zhong-fu, Yao Bing, Li Jing-wen, Linu Lin-zhong, Wang Jian-fang, Xu Bao-gen, On Incidence Graphs, ARS combinatoria 87 (2008), 213-223]. The origin of Incidence graphs can be traced to a paper titled Incidence and Strong edge colorings of graphs by R.A. Brualdi, et al. [Richard A. Brualdi and Jennifer J. Quinn Massey, Incidence and strong edge colorings of graphs, Discrete Mathematics 122 (1993) 51-58]. In this paper, we make a study of domination and related parameters in Incidence graphs.