Non-split and Inverse Non-split Domination Numbers in the Join and Corona of Graphs

Abstract

A dominating set D of a graph G = (V, E) is non-split dominating set if V \ D is connected. The non-split domination number of G is the minimum cardinality of a non-split dominating set in G. Let D be a minimum dominating set in G. If a subset D of V \ D is dominating in G, then D is called an inverse dominating set with respect to D. Furthermore, if V \ D is connected, then D is called an inverse non-split dominating set. The inverse non-split domination number of G is the minimum cardinality of an inverse non-split dominating set in G. In this paper, characterization of non-split dominating sets in the join and corona of two graphs are presented. Furthermore, explicit formulas for determining the non-split and inverse nonsplit domination numbers of these graphs are also determined.

Independent non-split domination in the join and corona of graphs

“…They obtained bounds on γ ns (G) and investigated relationship with other parameters. In [1], the inverse non-split domination in graphs was introduced and discussed; and in [3], the non-split dominating sets in the join and corona are characterized and the non-split and inverse non-split domination numbers of these graphs were determined. In this paper, the concept of independent nonsplit domination in graphs is revisited.…”