An optimal algorithm to find minimum k-hop connected dominating set of permutation graphs

Abstract

A set [Formula: see text] is said to be a [Formula: see text]-hop dominating set ([Formula: see text]-HDS) of a graph [Formula: see text] if every vertex [Formula: see text] is within [Formula: see text]-distances from at least one vertex [Formula: see text], i.e. [Formula: see text], where [Formula: see text] is a fixed positive integer. A dominating set [Formula: see text] is said to be minimum [Formula: see text]-hop connected dominating set of a graph [Formula: see text], if it is minimal as well as it is [Formula: see text]-HDS and the subgraph of G made by [Formula: see text] is connected. In this paper, we present an [Formula: see text]-time algorithm for computing a minimum [Formula: see text]-hop connected dominating set of permutation graphs with [Formula: see text] vertices.