On isolate-restrained total dominating sets in graphs

Abstract

In this paper, we study the notion of isolate-restrained total domination in finite simple graphs without isolated vertices. Fundamental properties of isolate-restrained total dominating sets are established and structural characteristics are discussed. Upper and lower bounds for the isolate-restrained total domination number are derived using standard graph parameters. Exact values of this parameter are obtained for several important classes of graphs such as paths, cycles, and complete graphs. Comparative relationships between isolate-restrained total domination and related domination parameters are analyzed. The results presented extend existing domination theory and provide new directions for further research in graph domination.