A set S ⊆ V (G) is a restrained strong resolving hop dominating in G if for every v ∈ (G)\S, there exists w such that dG(v, w) = 2 and or (G)\S has no isolated vertex. The smallest cardinality of set, denoted by γrsRh(G), called the domination number G. In this paper, we obtained corresponding parameter graphs resulting from join, corona lexicographic product two graphs. Specifically, character...

In a simple, finite and undirected graph G with vertex set V edge E, Prof. Sampathkumar defined degree equitability among vertices of G. Two u v are said to be equitable if |deg(u) − deg(v)| ≤ 1. Equitable domination has been studied in [7]. V.R.Kulli B.Janakiram strong non - split [12]. this paper, the version new type is

dominating set of G is called the strong complementary acyclic domination number of G and is denoted by ) (G st a c− γ . In this paper, we introduce and discuss the concept of strong complementary acyclic domination number of G.We determine this number for some standard graphs and obtain some bounds for general graphs. Its relationship with other graph theoretical parameters are also investigated.

In general strong domination number s(G) can be made to decrease or increase by removal of vertices from G. In this paper our main objective is the study of this phenomenon. Further the stability of the strong domination number of a graph G is investigated. 2000 Mathematics subject classification : 05C70

We discuss conditions such that strong stability and strong asymptotic compactness of a (discrete or continuous) semiflow defined on a subset in the positive cone of an ordered Banach space is preserved under asymptotic domination. This is used to show that on a Banach lattice with order continuous norm strong stability and almost periodicity of a (discrete or strongly continuous) semigroup of ...