The line graph associated to the total graph of a commutative ring
Abstract
Let R be a commutative ring with identity and T(Gamma(R)) its total graph. The subject of this article is the investigation of the properties of the corresponding line graph L(T(Gamma(R))). The classification of all commutative rings whose line graphs are planar or toroidal is given. It is shown that for every integer g >= 0 there are only finitely many commutative rings such that gamma(L(T(Gamma(R)))) = g.
Keywords:
Total graph / line graph / genus of a graph / commutative ringSource:
Ars Combinatoria, 2016, 127, 185195Funding / projects:
 Analysis and algebra with applications (RSMESTDBasic Research (BR or ON)174032)
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Institution/Community
GraFarTY  JOUR AU  Petrović, Zoran Z. AU  Pucanović, Zoran PY  2016 UR  https://grafar.grf.bg.ac.rs/handle/123456789/771 AB  Let R be a commutative ring with identity and T(Gamma(R)) its total graph. The subject of this article is the investigation of the properties of the corresponding line graph L(T(Gamma(R))). The classification of all commutative rings whose line graphs are planar or toroidal is given. It is shown that for every integer g >= 0 there are only finitely many commutative rings such that gamma(L(T(Gamma(R)))) = g. T2  Ars Combinatoria T1  The line graph associated to the total graph of a commutative ring EP  195 SP  185 VL  127 UR  https://hdl.handle.net/21.15107/rcub_grafar_771 ER 
@article{ author = "Petrović, Zoran Z. and Pucanović, Zoran", year = "2016", abstract = "Let R be a commutative ring with identity and T(Gamma(R)) its total graph. The subject of this article is the investigation of the properties of the corresponding line graph L(T(Gamma(R))). The classification of all commutative rings whose line graphs are planar or toroidal is given. It is shown that for every integer g >= 0 there are only finitely many commutative rings such that gamma(L(T(Gamma(R)))) = g.", journal = "Ars Combinatoria", title = "The line graph associated to the total graph of a commutative ring", pages = "195185", volume = "127", url = "https://hdl.handle.net/21.15107/rcub_grafar_771" }
Petrović, Z. Z.,& Pucanović, Z.. (2016). The line graph associated to the total graph of a commutative ring. in Ars Combinatoria, 127, 185195. https://hdl.handle.net/21.15107/rcub_grafar_771
Petrović ZZ, Pucanović Z. The line graph associated to the total graph of a commutative ring. in Ars Combinatoria. 2016;127:185195. https://hdl.handle.net/21.15107/rcub_grafar_771 .
Petrović, Zoran Z., Pucanović, Zoran, "The line graph associated to the total graph of a commutative ring" in Ars Combinatoria, 127 (2016):185195, https://hdl.handle.net/21.15107/rcub_grafar_771 .
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