On the genus of the intersection graph of ideals of a commutative ring
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.
Keywords:
Intersection graph / commutative rings / graph embeddingsSource:
Journal of Algebra and Its Applications, 2014, 13, 5Funding / projects:
- Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security (RS-MESTD-Basic Research (BR or ON)-174008)
DOI: 10.1142/S0219498813501557
ISSN: 0219-4988
WoS: 000332117600011
Scopus: 2-s2.0-84897607012
Collections
Institution/Community
GraFarTY - 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 . .