Equal eccentric domination in graphs

A subset $S$ of $V$ in a graph $G=(V, E)$ is called an equal eccentric dominating set(eed-set) if $S$ is a dominating set and $\forall y \in V-S, \exists$ at least one equal eccentric vertex $x$ of $y$ in $S$. In this paper, equal eccentric vertex, equal eccentric set, equal eccentric dominating set and equal eccentric domination numbers are defined. The equal eccentric domination numbers of various standard graphs are obtained and the bounds on equal eccentric domination numbers are also obtained and theorems related to this concepts are stated and proved.