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 ofG. In [7], Pushpam and Suseendran paper’s "Secure Restrained Domination in Graphs" studied few properties of secure restrained domination number of certain classes of graphs and evaluate γsr(G) values for trees, unicyclic graphs, split graphs and generalized Petersen graphs. In this paper, we characterize the secure restrained dominating sets in the join and corona of two graphs and give some important results. © Research India Publications.
Department of Mathematics, School of Arts and Sciences, University of San Carlos, Cebu City, 6000, Philippines
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