A1 Refereed original research article in a scientific journal
The metric dimension for resolving several objects
Authors: Laihonen T
Publisher: ELSEVIER SCIENCE BV
Publication year: 2016
Journal: Information Processing Letters
Journal name in source: INFORMATION PROCESSING LETTERS
Journal acronym: INFORM PROCESS LETT
Volume: 116
Issue: 11
First page : 694
Last page: 700
Number of pages: 7
ISSN: 0020-0190
eISSN: 1872-6119
DOI: https://doi.org/10.1016/j.ipl.2016.06.002
Abstract
A set of vertices S is a resolving set in a graph if each vertex has a unique array of distances to the vertices of S. The natural problem of finding the smallest cardinality of a resolving set in a graph has been widely studied over the years. In this paper, we wish to resolve a set of vertices (up to l vertices) instead of just one vertex with the aid of the array of distances. The smallest cardinality of a set S resolving at most l vertices is called l-set-metric dimension. We study the problem of the l-set-metric dimension in two infinite classes of graphs, namely, the two dimensional grid graphs and the n-dimensional binary hypercubes. (C) 2016 Elsevier B.V. All rights reserved.
A set of vertices S is a resolving set in a graph if each vertex has a unique array of distances to the vertices of S. The natural problem of finding the smallest cardinality of a resolving set in a graph has been widely studied over the years. In this paper, we wish to resolve a set of vertices (up to l vertices) instead of just one vertex with the aid of the array of distances. The smallest cardinality of a set S resolving at most l vertices is called l-set-metric dimension. We study the problem of the l-set-metric dimension in two infinite classes of graphs, namely, the two dimensional grid graphs and the n-dimensional binary hypercubes. (C) 2016 Elsevier B.V. All rights reserved.
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