Eccentric domination number of some cycle related graphs

Abstract

In a graph G, a vertex u is said to be an eccentric vertex of a vertex v if the distance between u and v is equals to the eccentricity of vertex v. A dominating set D of a graph G=(V,E) is said to be an eccentric dominating set if for every v∈V−D, there exists at least one eccentric vertex of v in D. The minimum cardinality of the minimal eccentric dominating sets of graph G is said to be eccentric domination number, denoted by γ ed (G). The eccentric domination numbers of some cycle related graphs have been investigated.