Document Type : Research Articles

Authors

• Fateme Movahedi ¹
• Mohammad hadi Akhbari ²

¹ Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran.

² Department of Mathematics, Estahban Branch, Islamic Azad University, Estahban, Iran.

Abstract

The edge neighborhood graph N_{e}(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 (N_e{}(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.

Keywords

• Edge neighborhood graph
• Domination number
• Total domination
• Independent domination
• 2-domination polynomial