A1 Refereed original research article in a scientific journal

On {l}-Metric Dimensions in Graphs




AuthorsHakanen A, Laihonen T

PublisherIOS PRESS

Publication year2018

JournalFundamenta Informaticae

Journal name in sourceFUNDAMENTA INFORMATICAE

Journal acronymFUND INFORM

Volume162

Issue2-3

First page 143

Last page160

Number of pages18

ISSN0169-2968

eISSN1875-8681

DOIhttps://doi.org/10.3233/FI-2018-1718


Abstract
A subset S of vertices is a resolving set in a graph if every vertex has a unique array of distances to the vertices of S. Consequently, we can locate any vertex of the graph with the aid of the distance arrays. The problem of finding the smallest cardinality of a resolving set in a graph has been widely studied over the years. In this paper, we consider sets S which can locate several, say up to l, vertices in a graph. These sets are called {l}-resolving sets and the smallest cardinality of such a set is the {l}-metric dimension of the graph. In this paper, we will give the {l}-metric dimensions for trees and king grids. We will show that there are certain vertices that necessarily belong to an {l}-resolving set. Moreover, we will classify all graphs whose {l}-metric dimension equals l.



Last updated on 2024-26-11 at 22:54