Integer Programming Formulations and Probabilistic Bounds for Some Domination Parameters

Abstract

In this paper, we further study the concepts of hop domination and 2-step domination and introduce the concepts of restrained hop domination, total restrained hop domination, 2-step restrained domination, and total 2-step restrained domination in graphs. We then construct integer programming formulations and present probabilistic upper bounds for these domination parameters.