| Title |
Total Perfect Hop Domination in Graphs Under Some Binary Operations |
|
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 |
|
Mindanao State
University - Iligan Institute of Technology