Perfect essential graphs

Authors

  • Abdolreza Azadi K. N. Toosi University of Technology, Iran
  • M. Javad Nikmehr K. N. Toosi University of Technology, Iran
  • B. Soleymanzadeh K. N. Toosi University of Technology, Iran

Abstract

Let R be a commutative ring with identity, and let Z(R) be the set of zero-divisors of R. Let EG(R) be a simple undirect graph associated with R whose vertex set is the set of all nonzero zero-divisors of R and and two distinct vertices x, y in this graph are joined by an edge if and only if AnnR(xy) is an essential ideal. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. In this paper, we characterize all rings whose EG(R) is perfect.

Downloads

Published

2019-11-22

Issue

Vol. 74 No. 2 (2019)

Section

Articoli

License

The authors retain all rights to the original work without any restrictions.

License for Published Contents

Licenza Creative Commons

"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).

Licence scheme | Legal code

License for Metadata

"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Licence scheme | Legal code

No Fee Charging

No fee is required to complete the submission/review/publishing process of authors paper.