On the Connected Distance–k Domination Numbers of Standard Graphs

Abstract

This paper investigates connected distance-k dominating sets in graphs, in which every vertex is within distance k from a connected dominating set. The connected distance- k domination number, denoted ck(G), represents the minimal cardinality of a minimal connected distance- k dominating set. The difference between the connected distance- k domination number and the standard distance- k domination number is expressed as ck(G)=ck(G)-k(G), which is referred to as the connected distance- k domination transition number. Various constraints on the connected distance- k domination number and its transition number have been established. For a number of common graphs, the precise values of these recently created parameters are calculated, and their connections to other dominating parameters are also investigated. Furthermore, results of the Nordhaus-Gaddum type are given for these new parameters.