Geodesic
The Planar Index and Outerplanar Index of Some Graphs Associated to Commutative Rings
Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 1, pp. 55-68.

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In this paper, we study the planar and outerplanar indices of some graphs associated to a commutative ring. We give a full characterization of these graphs with respect to their planar and outerplanar indices when R is a finite ring.
Keywords: Jacobson graph, commutative ring, planar index, outerplanar index 
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Barati, Zahra; Afkhami, Mojgan. The Planar Index and Outerplanar Index of Some Graphs Associated to Commutative Rings. Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 1, pp. 55-68. http://geodesic.mathdoc.fr/item/DMGAA_2019_39_1_a4/

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