CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

The Metric Dimension of the Total Graph of a Finite Commutative Ring

  Published:2016-04-11
 Printed: Dec 2016
  • David Dol┼żan,
    Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
Format:   LaTeX   MathJax   PDF  

Abstract

We study the total graph of a finite commutative ring. We calculate its metric dimension in the case when the Jacobson radical of the ring is nontrivial and we examine the metric dimension of the total graph of a product of at most two fields, obtaining either exact values in some cases or bounds in other, depending on the number of elements in the respective fields.
Keywords: total graph, finite ring, metric dimension total graph, finite ring, metric dimension
MSC Classifications: 13M99, 05E40 show english descriptions None of the above, but in this section
Combinatorial aspects of commutative algebra
13M99 - None of the above, but in this section
05E40 - Combinatorial aspects of commutative algebra
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/