On Resolving Hop Domination in Graphs

  • Jerson Saguin Mohamad Department of Mathematics and Statistics, College of Science and Mathematiccs, Western Mindanao State University, 7000 Zamboanga City, Philippines
  • Helen M. Rara Department of Mathematics and Statistics, College of Science and Mathematics, Center of Graph Theory, Algebra, and Analysis-Premier Research Institute of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines
Keywords: resolving hop dominating set, resolving hop domination number, join, corona, lexicograhic product

Abstract

A set S of vertices in a connected graph G is a resolving hop dominating set of G if S is a resolving set in G and for every vertex v ∈ V (G) \ S there exists u ∈ S such that dG(u, v) = 2. The smallest cardinality of such a set S is called the resolving hop domination number of G. This paper presents the characterizations of the resolving hop dominating sets in the join, corona and lexicographic product of two graphs and determines the exact values of their corresponding resolving hop domination number.

Published
2021-08-05
Section
Nonlinear Analysis