A Survey on Characterizing Trees Using Domination Number

Abstract

Ever since the discovery of domination numbers by Claude Berge in the year 1958, graph domination has become an important domain in graph theory that has strengthened itself as a theory and has extended its contributions to various applications. Tree characterization is an important problem in graph domination. This survey focuses on presenting a collection of results on characterizing trees using domination number.

On the Strong Secure Domination Number of a Graph

“…In this section, we give a necessary and sufficient condition for a tree to have a secure domination number less than or equal to 4. A survey on the constructive characterization of trees using different types of domination numbers was recently provided by the authors in [13].…”