Further results on secure restrained domination in graphs. (3rd March 2016) - Pushpam, P. Roushini Leely; Suseendran, Chitra
Abstract: Let G =( V, E ) be a graph and let S ⊆ V. The set S is a dominating set of G if every vertex in V \ S is adjacent to some vertex in S . The set S is a restrained dominating set if every vertex in V \ S is adjacent to a vertex in S and to a vertex in V \ S . The minimum cardinality of a restrained dominating set is called restrained domination number of G and it is denoted by γ r ( G ). A set S ⊆ V ( G ) is called a secure (restrained) dominating set if S is (restrained) dominating and for all u ϵ V \ S there exists v ϵ S ∩ N ( u ) such that ( S \ { v }) ∪ { u } is (restrained) dominating. The minimum cardinality of a secure (restrained) dominating set is a secure (restrained) domination number of G and it is denoted by γ s ( G ) (γ sr ( G )). In this paper we characterize few classes of graphs for which γ r ( G )=γ sr ( G ) and γ s ( G )=γ sr ( G ). Specific values of certain graphs are determined and Nordhaus Gaddum type results are discussed.