J-Domination in Graphs

Abstract

Let G be a graph. A subset D = {d1, d2, , dm} of vertices of G is called a J-set if NG[di] \ NG[dj ]/= ø for every i/= j, where i, j ∈ {1, 2, . . . ,m}. A J-set is called a J-dominating set of G if D = {d1, d2, . . . , dm} is a dominating set of G. The J-domination number of G, denoted by γJ (G), is the maximum cardinality of a J-dominating set of G. In this paper, we introduce this new concept and we establish formulas and properties on some classes of graphs and in join of two graphs. Upper and lower bounds of J-domination parameter with respect to the order of a graph and other parameters in graph theory are obtained. In addition, we present realization result involving this parameter and the standard domination. Moreover, we characterize J-dominating sets in some classes of graphs and join of two graphs and finally determine the exact value of the parameter of each of these graphs.