Marriage Domination and Divorce Domination in Graphs

Authors: Mark L. Caay, Rodolfo E. Maza

Abstract:

In this paper, the authors define two new variants of domination in graphs: the marriage and the divorce domination. A subset S ⊆ V (G) is said to be a marriage dominating set of G if for every e ∈ E(G), there exists a u ∈ V (G) such that u is one of the end vertex of e. A marriage dominating set S ⊆ V (G) is said to be a divorce dominating set of G if G\S is a disconnected graph. In this study, the authors present conditions of graphs for which the marriage and the divorce domination will take place and for which the two sets will coincide. Furthermore, the author gives the necessary and sufficient conditions for marriage domination to avoid divorce.

Keywords: domination, decomposition, marriage domination, divorce domination, marriage theorem