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Journal

Title Total Perfect Hop Domination in Graphs Under Some Binary Operations
Posted by Helen Rara
Authors Raicah C. Rakim and Helen M. Rara
Publication date July, 2021
Journal European Journal of Pure and Applied Mathematics
Volume 14
Issue No. 3, 2021
Pages 803-815
Publisher New York Business Global
Abstract Let G = (V (G), E(G)) be a simple graph. A set S subset of V (G) is a perfect hop dominating set of G if for every vertex v outside S, there is exactly one vertex u in S such that dG(u, v) = 2. The smallest cardinality of a perfect hop dominating set of G is called the perfect hop domination number of G, denoted by ph(G). A perfect hop dominating set S of V (G) is called a total perfect hop dominating set of G if for every v in V (G), there is exactly one vertex u in S such that dG(u, v) = 2. The total perfect hop domination number of G, denoted by tph(G), is the smallest cardinality of a total perfect hop dominating set of G. Any total perfect hop dominating set of G of cardinality tph(G) is referred to as a tph-set of G. In this paper, we characterize the total perfect hop dominating sets in the join, corona and lexicographic product of graphs and determine their corresponding total perfect hop domination number.
Index terms / Keywords total perfect hop domination, total perfect point-wise non-domination, perfect total (1, 2)*-domination, join, corona, lexicorgraphic
DOI https;//doi.org/10.29020/nybg.ejpam.v14i3.3975
URL http://www.ejpam.com