Degree equitable line domination in graphs

Abstract

A line dominating set D \subset V(L(G)) is called a degree equitable line dominating set, if for every vertex v \in V(L(G))-D there exists a vertex u \in D such that uv \in E in L(G) and |deg(u)-deg(v)| \leq 1. The minimum cardinality of vertices in such a set is called a degree equitable line dominating set in L(G) and is denoted byγ(G). In this paper, we study the graph theoretic properties ofγ(G) and many bounds were obtained in terms of elements of G and its relationships with other domination parameters were found.