Fractional distance domination in graphs

Abstract

Let G = (V,E) be a connected graph and let k be a positive integer with k ≤ rad(G). A subset D ⊆ V is called a distance k-dominating set of G if for every v ∈ V − D, there exists a vertex u ∈ D such that d(u,v) ≤ k. In this paper we study the fractional version of distance k-domination and related parameters.