To each commutative ring R one can associate the graph G(R), called the intersection graph of ideals, whose vertices are nontrivial ideals of R. In this paper, we try to establish some connections between commutative ring theory and graph theory, by study of the genus of the intersection graph of ideals. We classify all graphs of genus 2 that are intersection graphs of ideals of some commutative rings and obtain some lower bounds for the genus of the intersection graph of ideals of a nonlocal commutative ring.
TY - JOUR
AU - Pucanović, Zoran
AU - Radovanović, Marko
AU - Erić, Aleksandra
PY - 2014
UR - https://grafar.grf.bg.ac.rs/handle/123456789/636
AB - To each commutative ring R one can associate the graph G(R), called the intersection graph of ideals, whose vertices are nontrivial ideals of R. In this paper, we try to establish some connections between commutative ring theory and graph theory, by study of the genus of the intersection graph of ideals. We classify all graphs of genus 2 that are intersection graphs of ideals of some commutative rings and obtain some lower bounds for the genus of the intersection graph of ideals of a nonlocal commutative ring.
T2 - Journal of Algebra and Its Applications
T1 - On the genus of the intersection graph of ideals of a commutative ring
IS - 5
VL - 13
DO - 10.1142/S0219498813501557
ER -
@article{
author = "Pucanović, Zoran and Radovanović, Marko and Erić, Aleksandra",
year = "2014",
abstract = "To each commutative ring R one can associate the graph G(R), called the intersection graph of ideals, whose vertices are nontrivial ideals of R. In this paper, we try to establish some connections between commutative ring theory and graph theory, by study of the genus of the intersection graph of ideals. We classify all graphs of genus 2 that are intersection graphs of ideals of some commutative rings and obtain some lower bounds for the genus of the intersection graph of ideals of a nonlocal commutative ring.",
journal = "Journal of Algebra and Its Applications",
title = "On the genus of the intersection graph of ideals of a commutative ring",
number = "5",
volume = "13",
doi = "10.1142/S0219498813501557"
}
Pucanović, Z., Radovanović, M.,& Erić, A.. (2014). On the genus of the intersection graph of ideals of a commutative ring. in Journal of Algebra and Its Applications, 13(5).
https://doi.org/10.1142/S0219498813501557
Pucanović Z, Radovanović M, Erić A. On the genus of the intersection graph of ideals of a commutative ring. in Journal of Algebra and Its Applications. 2014;13(5).
doi:10.1142/S0219498813501557 .
Pucanović, Zoran, Radovanović, Marko, Erić, Aleksandra, "On the genus of the intersection graph of ideals of a commutative ring" in Journal of Algebra and Its Applications, 13, no. 5 (2014),
https://doi.org/10.1142/S0219498813501557 . .
