Graph Critical with Respect to Variants of Domination

Graph Critical with Respect to Variants of Domination

Introduction to Extended Total Domination, Independent Domination-Vertex Covering, Total K,K-Tuple, K-Dependent, Perfect Domination

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Chapter-0 provides an introduction to domination and its variants. Some fundamental results regarding domination and its variants, and historical background of domination In chapter-1 we define the concept of extended and total extended number for any graph. We also characterized those vertices whose removal increases or decreases or does not change extended total domination number of a graph. Chapter-2 contains the concept of independent domination and vertex covering of a graph.We prove that vertex covering number of graph never increase when a vertex is removed from the graph. We prove that...