Some binary products and integer linear programming for k-metric dimension of graphs

•k-metric dimension is an invariant in graphs which is difficult to compute and frequently arise in applications.•In this paper k-metric dimension of graphs is studied under some graph operations which are in turn suitable tools to approach NP-hard graph problems.•Also, an integer linear programming...

Full description

Saved in:

Bibliographic Details
Published in:	Applied mathematics and computation Vol. 409; p. 126420
Main Authors:	Klavžar, Sandi, Rahbarnia, Freydoon, Tavakoli, Mostafa
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.11.2021
Subjects:	[formula omitted]-metric dimension Binary product Chemical graph theory Integer linear programming Metric dimension 05C76 05C12 Metric dimension Binary product Integer linear programming k-metric dimension Chemical graph theory
ISSN:	0096-3003, 1873-5649
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	•k-metric dimension is an invariant in graphs which is difficult to compute and frequently arise in applications.•In this paper k-metric dimension of graphs is studied under some graph operations which are in turn suitable tools to approach NP-hard graph problems.•Also, an integer linear programming model for computing the k-metric dimension as well as a k-metric basis of a given graph is proposed. A sharp upper bound and a closed formula for the k-metric dimension of the hierarchical product of graphs is proved. Also, sharp lower bounds for the k-metric dimension of the splice and link products of graphs are presented. An integer linear programming model for computing the k-metric dimension as well as a k-metric basis of a given graph is proposed. These results are applied to bound or to compute the k-metric dimension of some classes of graphs that are of interest in mathematical chemistry.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2021.126420