Formulas and Properties of 2-Hop Domination in Some Graphs (European Journal of Pure and Applied Mathematics, 2024)
In this paper, 2-hop domination parameter is introduced and investigated on some special graphs and on the join of two graphs. Characterizations of 2-hop dominating sets in some special graphs are formulated to derive bounds or formulas of the parameter of these graphs. Moreover, new variant of pointwise non-domination is introduced to characterize 2-hop dominating sets in the join of two graphs. This characterization is used to calculate the exact value of 2-hop domination number of the join of two graphs.
Keywords: 2-hop dominating set; 2-hop domination number