A note on some parameters of domination on the edge neighborhood graph of a graph

The edge neighborhood graph Ne(G) of a simple graph G is the graph with the vertex set E ∪ S where S is the set of all open edge neighborhood sets of G and two vertices u, v ∈ V (Ne(G)) adjacent if u ∈ E and v is an open edge neighborhood set containing u. In this paper, we determine the domination number, the total domination number, the independent domination number and the 2-domination number in the edge neighborhood graph. We also obtain a 2-domination polynomial of the edge neighborhood graph for some certain graphs.