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A generalization of total graphs of modules

Year 2017, , 28 - 38, 11.07.2017
https://doi.org/10.24330/ieja.325918

Abstract

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.
 

References

  • 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.
Year 2017, , 28 - 38, 11.07.2017
https://doi.org/10.24330/ieja.325918

Abstract

References

  • 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.
There are 5 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Articles
Authors

Ahmad Abbasi

Leila Hamidian Jahromi This is me

Publication Date July 11, 2017
Published in Issue Year 2017

Cite

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. July 2017;22(22):28-38. doi:10.24330/ieja.325918
Chicago Abbasi, Ahmad, and Leila Hamidian Jahromi. “A Generalization of Total Graphs of Modules”. International Electronic Journal of Algebra 22, no. 22 (July 2017): 28-38. https://doi.org/10.24330/ieja.325918.
EndNote Abbasi A, Jahromi LH (July 1, 2017) A generalization of total graphs of modules. International Electronic Journal of Algebra 22 22 28–38.
IEEE A. Abbasi and L. H. Jahromi, “A generalization of total graphs of modules”, IEJA, vol. 22, no. 22, pp. 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 (July 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 and Leila Hamidian Jahromi. “A Generalization of Total Graphs of Modules”. International Electronic Journal of Algebra, vol. 22, no. 22, 2017, pp. 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.