# Total Perfect Hop Domination in Graphs Under Some Binary Operations

## Authors

• Raicah Cayongcat Rakim Mindanao State University
• Helen M Rara Mindanao State University, Iligan institute of Technology

## Abstract

Let G = (V (G), E(G)) be a simple graph. A set S âŠ† V (G) is a perfect hop dominating set of G if for every v âˆˆ V (G) \ S, there is exactly one vertex u âˆˆ 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 Î³ph(G). A perfect hop dominating set S âŠ† V (G) is called a total perfect hop dominating set of G if for every v âˆˆ V (G), there is exactly one vertex u âˆˆ S such that dG(u, v) = 2. The total perfect hop domination number of G, denoted by Î³tph(G), is the smallest cardinality of a total perfect hop dominating set of G. Any total perfect hop dominating set of G of cardinality Î³tph(G) is referred to as a Î³tph-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.

## Author Biographies

• Raicah Cayongcat Rakim, Mindanao State University
Associate Professor, Math Department, CNSM, MSU-Main Campus, Marawi City
• Helen M Rara, Mindanao State University, Iligan institute of Technology
Professor, Department of Mathematics and Statistic, Clollege of Science and Mathematics, MSU-Iligan Institute of Technology, Iligan City

2021-08-05

## Section

Nonlinear Analysis

## How to Cite

Total Perfect Hop Domination in Graphs Under Some Binary Operations. (2021). European Journal of Pure and Applied Mathematics, 14(3), 803-815. https://doi.org/10.29020/nybg.ejpam.v14i3.3975