Strong Regular Domination in Litact Graphs

Abstract

Strong regular domination in a litact graph is a novel domination parameter that has been introduced in this paper. A dominating set D⊆V(G) is known as Strong regular dominating set of G, if for each point x∈V(G)-D there is a vertex y∈D with an edge xy∈E(G) and deg⁡(x)≤deg⁡(y) and all vertices of 〈D〉 holds the equal degree. The lowest cardinality of such vertices of D is known as strong regular domination number of G which is represented by γ_str (G). The current study aims by taking strong regular domination on a litact graph m(G) denoted by  γ_str [m(G)]  and to obtain some bounds on γ_str [m(G)]  in terms of various parameters of G such as vertices, edges, maximum degree, diameter and so on and also in terms of various domination parameters of G such as total domination of G, connected domination of G and so on. Furthermore, outcomes resembling those of Nordhaus-Gaddum were also obtained.