Edward M. Kiunisala, Enrico L. Enriquez
Let G be a connected simple graph. A restrained dominating set S of the vertex set of G, V (G), is a secure restrained dominating set of G if for each u ∊ V (G) \ S, there exists v ∊ S such that uv ∊ E(G) and the set (S \ {v}) ⋃ {u} is a restrained dominating set of G. The minimum cardinality of a secure restrained dominating set of G, denoted by γsr (G), is called the secure restrained domination number of G. A secure restrained dominating set of cardinality γsr (G) is called a γsr -set of G. A secure restrained dominating set S of the vertex set of G is an inverse secure restrained dominating set if S ⊆ V (G) \ D where D is a minimum secure restrained dominating set of G. The minimum cardinality of an inverse secure restrained dominating set of G, denoted by γsr-1(G), is called an inverse secure restrained domination number of G. A secure restrained dominating set of cardinality γsr-1(G) is called a γsr-1-set of G. In this paper, we characterize the inverse secure restrained dominating sets in the join and corona of two graphs and give some important results. © Research India Publications.
Mathematics Department, College of Arts and Sciences, Cebu Normal University, Philippines; Mathematics Department, School of Arts and Sciences, University of San Carlos, Philippines
