We review a characterization of domination perfect graphs in terms of forbidden induced subgraphs obtained by Zverovich and Zverovich [12] using a computer code. Then we apply it to a problem of unique domination in graphs recently proposed by Fischermann and Volkmann. 1 Domination perfect graphs Let G be a graph. A set D ⊆ V (G) is a dominating set of G if each vertex of G either belongs to D ...

For a simple graph G, the independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. We establish upper bounds for the independent domination number of K1,k+1-free graphs, as functions of the order, size and k. Also we present a lower bound for the size of connected graphs with given order and value of independent domination ...

Abstract By suitably adjusting the tropical algebra technique we compute rainbow independent domination numbers of several infinite families graphs including Cartesian products $$C_n \Box P_m$$ C n ? P m </mm...

Domination and 2-domination numbers are defined only for graphs with non-isolated vertices. In a Graph G = (V, E) each vertex is said to dominate every in its closed neighborhood. graph G, subset S of V(G) called 2-dominating set if v ∈ V, V-S has atleast two neighbors S. The smallest cardinality known as the number γ2(G). this paper, we find some special also graphs.

In this paper we focus on 2- domination number of a fuzzy graph G by using effective edge and is denoted γ2(G) obtain some results concept, the relationship between other concepts are obtained.

A triangle-free graph is maximal if the addition of any edge produces a triangle. A set S of vertices in a graph G is called an independent dominating set if S is both an independent and a dominating set of G. The independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. In this paper, we show that i(G) ≤ δ(G) ≤ n 2 for maximal triangle-free graph...

Let f be a function that assigns to each vertex a subset of colors chosen from a set C = {1, 2, . . . , k} of k colors. If  u∈N(v) f (u) = C for each vertex v ∈ V with f (v) = ∅, then f is called a k-rainbow dominating function (kRDF) of G where N(v) = {u ∈ V | uv ∈ E}. The weight of f , denoted by w(f ), is defined as w(f ) =  v∈V |f (v)|. Given a graph G, the minimum weight among all weight...