Abstract

Let G = (V, E) be a simple graph. A subset D of V (G) is called a dominating set of G if for every v ∈ V – D, there exists u ∈ D such that u and v are adjacent. The minimum cardinality of the dominating set is called the domination number and it is denoted by γ(G). The Restrained domination set of a graph is a dominating set in which every vertex in V – D is adjacent. Claude Berge defined k – extendable graphs as those in which any independent set of cardinality k is a part of a maximum independent set of the graph. Graphs which are 1 – extendable are called Berge graphs [4]. Analogous to k – extendable graphs, the concept of k γ - endowed graphs is introduced. In such graphs every dominating set of cardinality k contains a minimum dominating set of the graph. In this paper, k - γr enresdowed graph is introduced in which every restrained dominating set of cardinality k contains a minimum restrained dominating set. Some properties and results are found for the standard graphs and the enresdowedness property of graphs with even number of vertices is found.

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