The metric dimension for resolving several objects

: Laihonen T

Publisher: ELSEVIER SCIENCE BV

: 2016

: Information Processing Letters

: INFORMATION PROCESSING LETTERS

: INFORM PROCESS LETT

: 116

: 11

: 694

: 700

: 7

: 0020-0190

: 1872-6119

DOI: https://doi.org/10.1016/j.ipl.2016.06.002

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.

RevisedLMetricDimension.pdf