In a graph G = (V, E), a set D ⊂ V is a weak convex dominating(WCD) set if each vertex of V-D is adjacent to at least one vertex in D and d < D > (u, v) = d G (u, v) for any two vertices u, v in D. A weak convex dominating set D, whose induced graph < D > has no cycle is called acyclic weak convex dominating(AWCD) set. The domination number γ ac (G) is the smallest order of a acyclic weak conve...

Nordhaus-Gaddum results for weakly convex domination number of a graph G are studied.

A set S of vertices of a graph G = (V,E) is a dominating set if every vertex of V − S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G, and the domination subdivision number sdγ(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the domination number. Arumug...

A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination number γt(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in ...

A set S of vertices of a graph G= (V ,E) with no isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination number t(G) is the minimum cardinality of a total dominating set ofG. The total domination subdivision number sd t (G) is the minimum number of edges that must be subdivided in order to increase the total domination number. We ...