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

Integer Programming Formulations and Probabilistic Bounds for Some Domination Parameters