Graph equations for line graphs , middle graphs, total closed neighbourhood graphs and total closed edge neighbourhood graphs

Let G be a graph with vertex set V(G) , edge set E(G). For each vertex (or edge) of G, a new vertex is taken and the resulting set of vertices is denoted by V1(G) (or E1(G)) respectively. Let G and L(G) denote the complement graph and line graph of G. The middle graph M(G) as an intersection graph ...