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

Published online by Cambridge University Press:  20 November 2018

David Dolžan
David Dolžan*
Affiliation:
Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia e-mail: david.dolzan@fmf.uni-lj.si
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Abstract

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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

13M9905E40total graphfinite ringmetric dimension
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 4 , 01 December 2016 , pp. 748 - 759
Copyright
Copyright © Canadian Mathematical Society 2016

References

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