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

Canadian mathematical bulletin

David Dolžan¹ 

[1] Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

关键词: total graph;    finite ring;    metric dimension;   

DOI  :  10.4153/CMB-2016-015-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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, dependingon the number of elements in the respective fields.

【 授权许可】

Unknown