Bounds for out degree equitable domination numbers in graphs

Kuppusamy Markandan Dharmalingam

Let $G=(V,E)$ be a simple graph. Let $D$ be a dominating set and $u\in D$. The edges from $u$ to $V-D$ are called dominating edges. A dominating set $D$ is called \emph{outdegree equitable} if the difference between the cardinalities of the sets of dominating edges from any two points of $D$ is at most one. The minimum cardinality of an out degree equitable dominating set is called the outdegree equitable domination number and is denoted by $\gamma_e$. The existence of an outdegree equitable dominating set is guaranteed. Out degree equitable domination is introduced in this paper. Minimum, minimal, independent out-degree equitable dominating sets, out degree Equitable points and Equitable neighborhood numbers are defined and also obtained the bounds for $\gamma_e$.