A subset S of the vertices of a graph G is an outer-connected dominating set, if S is a dominating set of G and G − S is connected. The outer-connected domination number of G, denoted by γ̃c(G), is the minimum cardinality of an OCDS of G. In this paper we generalize the outer-connected domination in graphs. Many of the known results and bounds of outer-connected domination number are immediate c...

In this paper, we investigate domination number as well as signed domination numbers of Cay(G : S) for all cyclic group G of order n, where n in {p^m; pq} and S = { a^i : i in B(1; n)}. We also introduce some families of connected regular graphs gamma such that gamma_S(Gamma) in {2,3,4,5 }.

Abstract. In this paper, connected domination in fuzzy graphs using strong arcs is introduced. The strong connected domination number of different classes of fuzzy graphs is obtained. An upper bound for the strong connected domination number of fuzzy graphs is obtained. Strong connected domination in fuzzy trees is studied. It is established that the set of fuzzy cut nodes of a fuzzy tree is a ...

The concept of triple connected graphs with real life application was introduced in [7] by considering the existence of a path containing any three vertices of a graph G. In this paper, we introduce a new domination parameter, called Smarandachely triple connected domination number of a graph. A subset S of V of a nontrivial graph G is said to be Smarandachely triple connected dominating set, i...

A dominating setD ⊆ V of a graphG = (V,E) is said to be a connected cototal dominating set if 〈D〉 is connected and 〈V −D〉 6= ∅, contains no isolated vertices. A connected cototal dominating set is said to be minimal if no proper subset of D is connected cototal dominating set. The connected cototal domination number γccl(G) of G is the minimum cardinality of a minimal connected cototal dominati...