We consider two types of graph domination - {k}-domination and k-tuple domination, for a fixed positive integer k - and provide new NP-complete as well as polynomial time solvable instances for their related decision ...

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 ...

A biclique is a set of vertices that induce a complete bipartite graph. A graph G is biclique-Helly when its family of maximal bicliques satisfies the Helly property. If every induced subgraph of G is also biclique-Helly, ...

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 ...

Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set is a set of vertices such that every ...

Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set, also known as a k-tuple total 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 ...