Yıl 2017, Cilt 22, Sayı 22, Sayfalar 28 - 38 2017-07-11

A generalization of total graphs of modules

Ahmad Abbasi [1] , Leila Hamidian Jahromi [2]

82 211

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.
 

Commutative ring, total graph
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  • 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.
Konular Matematik
Dergi Bölümü Makaleler
Yazarlar

Yazar: Ahmad Abbasi

Yazar: Leila Hamidian Jahromi

Bibtex @araştırma makalesi { ieja325918, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {22}, pages = {28 - 38}, doi = {10.24330/ieja.325918}, title = {A generalization of total graphs of modules}, key = {cite}, author = {Jahromi, Leila Hamidian and Abbasi, Ahmad} }
APA Abbasi, A , Jahromi, L . (2017). A generalization of total graphs of modules. International Electronic Journal of Algebra, 22 (22), 28-38. DOI: 10.24330/ieja.325918
MLA Abbasi, A , Jahromi, L . "A generalization of total graphs of modules". International Electronic Journal of Algebra 22 (2017): 28-38 <http://dergipark.gov.tr/ieja/issue/30344/325918>
Chicago Abbasi, A , Jahromi, L . "A generalization of total graphs of modules". International Electronic Journal of Algebra 22 (2017): 28-38
RIS TY - JOUR T1 - A generalization of total graphs of modules AU - Ahmad Abbasi , Leila Hamidian Jahromi Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.325918 DO - 10.24330/ieja.325918 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 28 EP - 38 VL - 22 IS - 22 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.325918 UR - http://dx.doi.org/10.24330/ieja.325918 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra A generalization of total graphs of modules %A Ahmad Abbasi , Leila Hamidian Jahromi %T A generalization of total graphs of modules %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 22 %N 22 %R doi: 10.24330/ieja.325918 %U 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. http://dx.doi.org/10.24330/ieja.325918