Sub-Restrained Perfect Domination In Graphs

Abstract

et 𝐺=(𝑉(𝐺),𝐸(𝐺))be a connected graph. Let 𝑀⊆𝑉(𝐺)be a minimum perfect dominating set and 𝑇⊆𝑉(𝐺)\𝑀is said to be sub-restrained perfect dominating setof Gif every 𝑣∈𝑉(𝐺)∖𝑇such that|𝑁(𝑣)∩𝑇|=1. The sub-restrained perfect dominating number of 𝐺is the minimum cardinality of thesub-restrained perfect dominating set of 𝐺which is denoted by𝛾𝑠𝑟𝑝(G). As a novel approach to the study of domination theory, we can attempt to define sub-restrained perfect dominating set in this paper. We also identify certain novel findings, fundamental characteristics, and so forth.