Abstract

Let G be a graph with no isolated vertex. A set D ⊆ V(G) is a double outer-independent dominating set of G if V (G) \ D is an independent set and | N[υ] ∩ D| ≥ 2 for every v ϵ V(G), where N[υ] denotes the closed neighbourhood of v. The minimum cardinality among all double outer-independent dominating sets of G is the double outer-independent domination number of G. In this paper, we continue with the study of this parameter. For instance, we give some relationships that exist between this parameter and other domination invariants in graph. Also, we present tight bounds and show some classes of graphs for which the bounds are achieved. Finally, we provide closed formulas for the double outer-independent domination number of rooted product graphs, and characterize the graphs reaching these expressions.

摘要

令G为没有孤立顶点的图。如果V（G）\ D是一个独立集，并且| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |||||的组合关系）的组合来决定。N [υ]∩D | 对于每个v ϵ V（G）≥2，其中N [υ]表示v的封闭邻域。G的所有双重外部无关支配集合中的最小基数是G的双重外部无关支配数。 ，我们将继续研究此参数。例如，我们给出了该参数与图中其他支配不变量之间存在的一些关系。此外，我们提出了严格的界限，并显示了达到界限的某些图。最后，我们为有根积图的双重外部无关控制数提供封闭式，并对达到这些表达式的图进行特征化。