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For a graph G and a subset S of the vertex set V(G), denote by N_G[S] the set of vertices in G which are in S or adjacent to a vertex in S. If N_G[S]=V(G), then S is said to ...

A connected dominating set in a connected graph G is a dominating set in G whose vertices induce a connected subgraph, i.e., one in which there is no dominating vertex not ...

A minimum dominating set is a dominating set of smallest size in a given graph. The size of a minimum dominating set is known as the domination number of the graph. A minimum ...

A minimal dominating set is a dominating set in a graph that is not a proper subset of any other dominating set. Every minimum dominating set is a minimal dominating set, but ...

For a graph G and a subset S^t of the vertex set V(G), denote by N_G^t[S^t] the set of vertices in G which are adjacent to a vertex in S^t. If N_G^t[S^t]=V(G), then S^t is ...

An independent dominating set of a graph G is a set of vertices in G that is both an independent vertex set and a dominating set of G. The minimum size of an independent ...

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset). Members of a ...

The concept of irredundance was introduced by Cockayne et al. (1978). Let N_G[v] denote the graph neighborhood of a vertex v in a graph G (including v itself), and let N_G[S] ...

A maximal irredundant set is an irredundant set that cannot be expanded to another irredundant set by addition of any vertex in the graph. Note that a maximal irredundant set ...

Given a collection of sets, a member set that is not a proper subset of another member set is called a minimal set. Minimal sets are important in graph theory, since many ...