A Novel Approach on Energy of λJ-dominating Single-Valued Neutrosophic Graph Structure

Abstract

The concept of dominance is one of the most important ideas in graph theory for handling random events, and it has drawn the interest from many scholars. Research related to graph energy has garnered a lot focus recently. The application of single-valued neutrosophic graphs (SVNGs) for energy, Laplacian energy, and dominating energy has been recommended by previous studies. In this research, we apply the concepts of single-valued neutrosophic sets (SVNS) to graph structures (GSs) and investigate some intriguing features of single-valued neutrosophic graph structures (SVNGS). Moreover, the notions of λJ-dominating energy GS in an SVNGS environment are analyzed in this study. More specifically, illustrative examples are used to develop the adjacency matrix of a λJ-dominating SVNGS, as well as the spectrum of the adjacency matrix and their related theory. Further, the SVNGS λJ-dominating energy is determined. We go over various characteristics and constraints for the energy of SVNGS with λJ-dominating. Further, we introduce the idea of isomorphic and identical λJ-dominating SVNGS energy, which has been studied using relevant examples, and some of its established properties are presented.