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Title Restrained Perfect Domination in Graphs
Posted by Bernadette Tubo
Authors Tubo, Bernadette F. and Canoy, Sergio R. Jr.
Publication date 2015
Journal International Journal of Mathematical Analysis
Volume 9
Issue 25
Pages 1231-1240
Publisher HIKARI Ltd
Abstract Let G = (V (G),E(G)) be a connected graph. A dominating set S of a graph G is a perfect dominating set if every vertex of G not in S is adjacent to exactly one vertex in S. A subset S of V (G) is a restrained perfect dominating set of G if S is a perfect dominating set and if for every v 2 V (G)S, there exists z 2 V (G)S such that vz 2 E(G). The minimum cardinality of a restrained perfect dominating set of G, denoted by rp(G), is the restrained perfect domination number. In this paper, we characterize the restrained perfect domination sets in the join, corona and composition of graphs. We also determine the corresponding rp(G) of these graphs.
Index terms / Keywords domination, perfect domination, restrained domination, join, corona, composition