Point Set Domination in Uniform Single-Valued Neutrosophic Graphs for Energy-Efficient Backbone Design in Wireless Sensor Networks

Abstract

This paper introduces a novel framework for Point Set Domination in Uniform Single-Valued Neutrosophic Graphs (PS-USVNGs) and investigates its application to energy-efficient backbone design in Wireless Sensor Networks (WSNs). A Point Set Neutrosophic Strength (PNS) function, incorporating truth-membership, indeterminacy-membership, and falsity-membership values, is proposed to model domination under uncertainty. Based on this strength function, new concepts of Point Set USVNG domination, dominating sets, and domination numbers are formulated. Several membership-based properties are established to analyze the effects of truth, indeterminacy, and falsity on domination behavior. Furthermore, graph operation results involving union, join, Cartesian product, and complement operations are developed within the PS-USVNG framework. A uniformity theorem is also derived to characterize domination in uniform neutrosophic environments. The proposed model is applied to WSN backbone formation, enabling reliable and uncertainty-aware node selection. Comparative analysis demonstrates that the PS-USVNG approach provides a more comprehensive representation of uncertain communication networks than existing domination models.