Araştırma Makalesi
BibTex RIS Kaynak Göster

A generalization of total graphs of modules

Yıl 2017, Cilt: 22 Sayı: 22, 28 - 38, 11.07.2017
https://doi.org/10.24330/ieja.325918

Öz

Let $R$ be a commutative ring, and let $M\neq 0$ be an $R$-module with a non-zero proper submodule $N$, where $N^{\star}=N-\{0\}$.
 Let $\Gamma_{N^{\star}}(M)$ denote the (undirected) simple graph  with vertices $ \{x \in  M -N\,|\,x+x^\prime \in N^{\star}$ for some $x\neq x' \in M-N \}$, where distinct vertices $x$ and $y$ are adjacent if and only if  $x+y \in N^{\star}$. We determine some graph theoretic properties of $\Gamma_{N^{\star}}(M)$ and investigate  the  independence number and chromatic number.
 

Kaynakça

  • A. Abbasi and S. Habibi, The total graph of a commutative ring with respect to proper ideals, J. Korean Math. Soc., 49(1) (2012), 85-98.
  • A. Abbasi and S. Habibi, The total graph of a module over a commutative ring with respect to proper submodules, J. Algebra Appl., 11(3) (2012), 1250048 (13 pp).
  • D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra, 320(7) (2008), 2706-2719.
  • J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976.
  • S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra, 31(9) (2003), 4425-4443.
Yıl 2017, Cilt: 22 Sayı: 22, 28 - 38, 11.07.2017
https://doi.org/10.24330/ieja.325918

Öz

Kaynakça

  • A. Abbasi and S. Habibi, The total graph of a commutative ring with respect to proper ideals, J. Korean Math. Soc., 49(1) (2012), 85-98.
  • A. Abbasi and S. Habibi, The total graph of a module over a commutative ring with respect to proper submodules, J. Algebra Appl., 11(3) (2012), 1250048 (13 pp).
  • D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra, 320(7) (2008), 2706-2719.
  • J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976.
  • S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra, 31(9) (2003), 4425-4443.
Toplam 5 adet kaynakça vardır.

Ayrıntılar

Konular Matematik
Bölüm Makaleler
Yazarlar

Ahmad Abbasi

Leila Hamidian Jahromi Bu kişi benim

Yayımlanma Tarihi 11 Temmuz 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 22 Sayı: 22

Kaynak Göster

APA Abbasi, A., & Jahromi, L. H. (2017). A generalization of total graphs of modules. International Electronic Journal of Algebra, 22(22), 28-38. https://doi.org/10.24330/ieja.325918
AMA Abbasi A, Jahromi LH. A generalization of total graphs of modules. IEJA. Temmuz 2017;22(22):28-38. doi:10.24330/ieja.325918
Chicago Abbasi, Ahmad, ve Leila Hamidian Jahromi. “A Generalization of Total Graphs of Modules”. International Electronic Journal of Algebra 22, sy. 22 (Temmuz 2017): 28-38. https://doi.org/10.24330/ieja.325918.
EndNote Abbasi A, Jahromi LH (01 Temmuz 2017) A generalization of total graphs of modules. International Electronic Journal of Algebra 22 22 28–38.
IEEE A. Abbasi ve L. H. Jahromi, “A generalization of total graphs of modules”, IEJA, c. 22, sy. 22, ss. 28–38, 2017, doi: 10.24330/ieja.325918.
ISNAD Abbasi, Ahmad - Jahromi, Leila Hamidian. “A Generalization of Total Graphs of Modules”. International Electronic Journal of Algebra 22/22 (Temmuz 2017), 28-38. https://doi.org/10.24330/ieja.325918.
JAMA Abbasi A, Jahromi LH. A generalization of total graphs of modules. IEJA. 2017;22:28–38.
MLA Abbasi, Ahmad ve Leila Hamidian Jahromi. “A Generalization of Total Graphs of Modules”. International Electronic Journal of Algebra, c. 22, sy. 22, 2017, ss. 28-38, doi:10.24330/ieja.325918.
Vancouver Abbasi A, Jahromi LH. A generalization of total graphs of modules. IEJA. 2017;22(22):28-3.