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 ...

In this paper, we continue the investigation of different types of (Grundy) dominating sequences. We consider four different types of Grundy domination numbers and the related zero forcing numbers, focusing on these numbers ...

In 2008, a unified approach (labeled domination) to several domination problems (k-tuple domination, {k} -domination, and M-domination, among others) was introduced. The labeled domination problem is to find an L-dominating ...

A sequence of vertices in a graph is called a (total) legal dominating sequence if every vertex in the sequence (totally) dominates at least one vertex not dominated by the ones that precedes it, and at the end all vertices ...

A legal dominating sequence of a graph is an ordered dominating set of vertices where each element dominates at least another one not dominated by its predecessors in the sequence. The length of a largest legal dominating ...

Say that an edge of a graph G dominates itself and every other edge sharing a vertex of it. An edge dominating set of a graph G= (V, E) is a subset of edges E′⊆ E which dominates all edges of G. In particular, if every ...

Given a graph G = (V;E), a subset S V is 2-dominating if every vertex in S has at least two neighbors in S. The minimum cardinality of such a set is called the 2-domination number of G. Consider a process in discrete ...

A sequence of vertices in a graph G with no isolated vertices is called a total dominating sequence if every vertex in the sequence totally dominates at least one vertex that was not totally dominated by preceding vertices ...