Strong Regular Domination in Litact Graphs

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 γₛtr (G). The current study aims by taking strong regular domination on a litact graph m (G) denoted by γₛtr m (G) and to obtain some bounds on γₛtr 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.