Neighborhood Connected Domination Number of Total Graphs

Let G = (V, E) be a connected graph. A dominating set S of a connected graph G is called a neighborhood connected dominating set (ncd-set) if the induced subgraph (N(S)) of G is connected. The neighborhood connected domination number γ sub nc /sub (G) is the minimum cardinality of a ncd-set. The total graph T(G) of a graph G is a graph such that the vertex set of T(G) corresponds to the vertices and edges of G and two vertices are adjacent in T(G) if and only if their corresponding elements are either adjacent or incident in G. In this paper we study the concept of neighborhood connected domination in total graphs.