A dominating set S ⊆ V is said to be a restrained dominating set of graph G if every vertex not in S is adjacent to a vertex in S and also to a vertex in V − S. A set S ⊆ V is called an equitable dominating set if for ...

For a graph G = (V, E), a set S ⊆ V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V − S. The smallest cardinality of a restrained dominating set of G is called ...

For a graph G = (V,E), a subset D of E is restrained edge dominating set of G if every edge not in D is adjacent to an edge in D as well as an edge in E −D. The restrained edge domination number of G, denoted by γre(G) is ...

If G is a graph with vertex set V (G) then dominating set D⊆ V (G) is called total if every vertex of V (G) is adjacent to at least one vertex of D while it is called equitable if for every vertex u in V (G)− D there exists ...

A dominating set S ⊆ V (G)of a graph G is called restrained dominating set if every vertex in V (G) - S is adjacent to a vertex in S and to a vertex in V (G) - S. The restrained domination number of G, denoted by γ_r (G), ...

A vertex dominating set D of V (G) is called a chromatic transversal dominating set of G if D intersects every color class of G. The minimum cardinality of D is called a chromatic transversal domination number of G. In ...