Geodesic
Degree Equitable Domination on Graphs
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 1, p. 191

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A subset $D$ of $V$ is called an equitable dominating set if for every $v \in V-D $ there exists $a$ vertex $u n D$ such that $u v n E(G)$ and $eft| ẹg(u)-ẹg (v) \right| eq 1$, where $ẹg(u)$ denotes the degree of vertex $u$ and $ẹg(v)$ denotes the degree of vertex $v$. The minimum cardinality of such a dominating set is denoted by $\gamma^{e}$ and is called the equitable domination number of $G$. This Paper aims at the study of a new concept called degree equitable domination introduced by Prof. E. Sampathkumar. Minimal equitable dominating sets are characterized. The complexity of the new parameter namely equitable domination number is determined.
Classification : 05C
Keywords: Equitable Domination Number, Minimal Equitable Dominating set, Equitable isolate, Equitable independent set 
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V. Swaminathan; K. M. Dharmalingam. Degree Equitable Domination on Graphs. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 1, p. 191 . http://geodesic.mathdoc.fr/item/KJM_2011_35_1_a16/