Locating-Hop Domination in Graphs

Sergio R. Canoy; Jr.; Gemma P. Salasalan

doi:10.5666/KMJ.2022.62.1.193

Article

Kyungpook Mathematical Journal 2022; 62(1): 193-204

Published online March 31, 2022

Locating-Hop Domination in Graphs

Sergio R. Canoy, Jr.^*, Gemma P. Salasalan

Department of Mathematics and Statistics, College of Science and Mathematics, Center for Graph Theory, Algebra, and Analysis, Premier Research Institute of Science and Mathematics, MSU-Iligan Institute of Technology, Andres Bonifacio Ave., Iligan City, Philippines
e-mail : sergio.canoy@g.msuiit.edu.ph

Department of Arts and Sciences, Institute of Teacher Education, Arts and Sciences, Davao del Sur State College, Matti, Digos City, Davao del Sur
e-mail : gemma.salasalan@g.msuiit.edu.ph

Received: May 4, 2021; Revised: August 16, 2021; Accepted: October 7, 2021

Abstract

Go to

Abstract

A subset S of V(G), where G is a simple undirected graph, is a hop dominating set if for each v∈V(G)∖S, there exists w ∈ S such that dG(v,w)=2 and it is a locating-hop set if NG(v,2)∩S≠NG(v,2)∩S for any two distinct vertices u,v∈V(G)∖S. A set S⊆V(G) is a locating-hop dominating set if it is both a locating-hop and a hop dominating set of G. The minimum cardinality of a locating-hop dominating set of G, denoted by γlh(G), is called the locating-hop domination number of G. In this paper, we investigate some properties of this newly defined parameter. In particular, we characterize the locating-hop dominating sets in graphs under some binary operations.

Keywords: locating-hop, hop domination, complement-locating, complement locating-dominating