The problems of determining minimum identifying, locating-dominating, open locating-dominating or locating total-dominating codes in a graph G are variations of the classical minimum dominating set problem in G and are all ...

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 ...

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 ...

We prove that, in games in which all the guards move at the same turn, the eternal domination and the clique-connected cover numbers coincide for interval graphs. A linear algorithm for the eternal dominating set problem ...

Given a graph G = (V,E), a perfect dominating set is a subset of vertices V ⊆ V (G) such that each vertex v ∈ V (G) \ V is dominated by exactly one vertex v ∈ V . An efficient dominating set is a perfect dominating set V ...

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 ...