Algorithm of Secure Distance Matrix Dominating Sets in Graphs

Abstract

This paper introduces and investigates the concept of Secure Distance Matrix Dominating Sets (SDMDS) in graphs, a novel variation of dominating sets that combines security properties with distance matrix conditions. We establish fundamental properties, determine exact values for basic graph families, develop algorithmic approaches, and prove several theoretical results. The study encompasses both structural characteristics and computational aspects of SDMDS, providing a foundation for future research in this area. We present efficient algorithms for finding SDMDS in specific graph classes and establish bounds for various graph families.