Geodesic
The Metric Dimension of the Total Graph of a Finite Commutative Ring
Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 748-759

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DOI

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.
DOI : 10.4153/CMB-2016-015-5
Mots-clés : 13M99, 05E40, total graph, finite ring, metric dimension 
Dolžan, David. The Metric Dimension of the Total Graph of a Finite Commutative Ring. Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 748-759. doi: 10.4153/CMB-2016-015-5
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     author = {Dol\v{z}an, David},
     title = {The {Metric} {Dimension} of the {Total} {Graph} of a {Finite} {Commutative} {Ring}},
     journal = {Canadian mathematical bulletin},
     pages = {748--759},
     year = {2016},
     volume = {59},
     number = {4},
     doi = {10.4153/CMB-2016-015-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-015-5/}
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