Let G = (V, E) be a graph and u, v ~ V. Then, u strongly dominates v and v weakly dominates u if (i) uv ~ E and (ii) deg u >/deg v. A set D c V is a strong-dominating set (sd-set) of G if every vertex in V D is strongly dominated by at least one vertex in D. Similarly, a weak-dominating set (wd-set) is defined. The strong (weak) domination number 7s (7w) of G is the minimum cardinality of an sd...

Let G = (V,E) be a graph. A subset D ⊆ V is a total dominating set of G if for every vertex y ∈ V there is a vertex x ∈ D with xy ∈ E. A subset D ⊆ V is a strong dominating set of G if for every vertex y ∈ V − D there is a vertex x ∈ D with xy ∈ E and deg G (x) ≥ deg G (y). The total domination number γt(G) (the strong domination number γS(G)) is defined as the minimum cardinality of a total do...

The core of a market in indivisible goods can be defined in terms of strong domination or weak domination. The core defined by strong domination is always non-empty, but may contain points which are unstable in a dynamic sense. However, it is shown that there are always stable points in the core, and a characterization is obtained. The core defined by weak domination is always non-empty when th...

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