The line graph associated to the total graph of a commutative ring

Petrović, Zoran Z.; Pucanović, Zoran

2016

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Authors

Petrović, Zoran Z.
Pucanović, Zoran

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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 ring

Source:
Ars Combinatoria, 2016, 127, 185-195

Funding / projects:

Analysis and algebra with applications (RS-174032)

ISSN: 0381-7032

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GraFar

TY  - 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 = "195-185",
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, 185-195.
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;127:185-195.
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):185-195,
https://hdl.handle.net/21.15107/rcub_grafar_771 .