The complete cototal domination set is said to be irredundant dominating if for each u ∈ S, NG [S − {u}] ≠ [S]. minimum cardinality taken over all an called number and denoted by γircc(G). Here a new parameter was introduced the study of bounds γircc(G) initiated.

A set $S subseteq V(G)$ is a semitotal dominating set of a graph $G$ if it is a dominating set of $G$ andevery vertex in $S$ is within distance 2 of another vertex of $S$. Thesemitotal domination number $gamma_{t2}(G)$ is the minimumcardinality of a semitotal dominating set of $G$.We show that the semitotal domination problem isAPX-complete for bounded-degree graphs, and the semitotal dominatio...

Based on the concept of general domination structures, this paper presents an approach to model variable preferences for multicriteria optimization and decision making problems. The preference assumptions for using a constant convex cone are given, and, in remedy of some immanent model limitations, a new set of assumptions is presented. The underlying preference model is derived as a variable d...

A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...

Let G be an undirected connected graph with vertex and edge sets V (G) E(G), respectively. A set C ⊆ is called weakly convex hop dominating if for every two vertices x, y ∈ C, there exists x-y geodesic P(x, y) such that (P(x, y)) v (G)\C, w dG(v, w) = 2. The minimum cardinality of a G, denoted by γwconh(G), the domination number G. In this paper, we introduce initially investigate concept domin...

Suppose V is a finite set and C a collection of subsets of V that contains ∅ and V and is closed under taking intersections. Then the ordered pair (V, C) is called a convexity and the elements of C are referred to as convex sets. For a set S ⊆ V , the convex hull of S relative to C, denoted by CHC(S), is the smallest convex set containing S. The Caratheodory number, relative to a given convexit...