Eccentric domination number of some path related graphs

Abstract

In a graph G, a vertex u is said to be an eccentric vertex of a vertex v if d(u, v) = 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 of graph G which is denoted by γ ed (G). Here, exact value of γ ed (G) for some path related graphs, have been investigated.