Split Regular Domination in Litact Graphs

Abstract

Objectives: In the context of graph theory, a litact graph is a specific type of graph. This study introduces a new domination parameter, called split regular domination in litact graphs. Methods: When we talk about split regular domination in a litact graph during this investigation, we think about how to divide the litact graph into partitions that adhere to specific domination principles by taking a minimal split regular dominating set with all vertices of equal degree. We used a few common definitions and the ideas of several domination parameters in G to obtain the results. Findings: Numerous bounds on were found in relation to the different parameters of G like vertices, edges, diameter, vertex covering number, maximum degree and so forth, and its relationship to other dominating parameters of G such as total domination, edge domination, connected domination and so on was also found. Furthermore, outcomes resembling those of Nordhaus-Gaddum were also obtained. Novelty: Graph G was used to find a litact graph. Subsequently, a few findings of a new domination parameter called split regular domination in a litact graph in terms of different parameters of G have been established. Keywords: Graph, Litact Graph, Split Domination Number, Regular Domination Number, Split Regular Domination Number