### 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.

**Published:**2014-09-16

**How to Cite this Article:**M. H. Muddebiha, U. A. Panfarosh, Anil R. Sedamkar, Degree equitable line domination in graphs, Eng. Math. Lett., 2014 (2014), Article ID 19 Copyright © 2014 M. H. Muddebiha, U. A. Panfarosh, Anil R. Sedamkar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Engineering Mathematics Letters

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