Autor(es)

Flavia Bonomo and Boštjan Brešar and Luciano N Grippo and Martin Milanič and Martín D Safe

URL Pública

Abstract

In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination number, γ w 2 (G), the 2-domination number, γ 2 (G), the {2}-domination number, γ {2}(G), the double domination number, γ× 2 (G), the total {2}-domination number, γ t {2}(G), and the total double domination number, γ t× 2 (G), where G is a graph in which the corresponding invariant is well defined. The third criterion yields rainbow versions of the mentioned six parameters, one of which has already been well studied, and three other give new interesting parameters. Together with a special, extensively studied Roman domination, γ R (G), and two classical parameters, the domination number, γ (G), and the total domination number, γ t (G), we consider 13 domination …