The Connected Distance - K Domination Number of Some Families of Graphs

Abstract

distance - k dominating set  of a graph G = (V, E) is a connected distance - k dominating set if the induced sub-graph is connected. The connected distance -k domination number  of G is the minimum cardinality of a minimal connected distance - k dominating set of G.The connected distance - k domination transition number of a graph G is defined as and is denoted as In this paper, we defined the notion of connected distance - k domination and connected distance - k domination transition number in graphs. We got many bounds on connected distance - k dominationnumber and connected distance - k domination transition number. Exact values of these new parameters are obtained for some standard graphs and also their relationship with other domination parameters were obtained. Nordhaus - Gaddum type results were also obtained for these new parameters.