Research Article
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Z_n Halkası üzerinde nilpotent grafların laplasyan spektral özellikleri

Year 2017, Volume: 21 Issue: 6, 1443 - 1447, 01.12.2017

Sezer Sorgun Hatice Pınar Cantekin

https://doi.org/10.16984/saufenbilder.277822

Abstract

 birimli bir halka
olsun. ' nin  ile gösterilen
nilpotent grafı,  noktalar kümesi ve ,  halkasının bütün
nilpotent elemanlarının kümesi olmak üzere; “iki farklı  ve  noktaları komşudur ” önermesini sağlayan kenarlar kümesinden oluşur. Bu
makalede  halkası üzerinde
tanımlanan nilpotent grafın Laplasyan spektral özellikleri incelenmektedir.

Keywords

Nilpotent graph Laplasyan Spektrum

References

  • [1]. D.F. Anderson, P.S. Livingston, "The zero-divisor graph of a commutative ring", J. Algebra, vol. 217, pp. 434-447, 1999.
  • [2]. D.F. Anderson, A. Badawi, "The total graph of a commutative ring", J. Algebra, vol. 320, pp. 2706-2719, 2008.
  • [3]. M.J.Nikmehr, S.Khojasteh, "On the nilpotent graph of a ring", Turkish Journal of Mathematics, vol. 37, pp. 553-559, 2013.
  • [4]. P. Sharma, A.Sharma, R.K. Vats, "Analysis of Adjacency Matrix and Neighborhood Associated with Zero Divisor Graph of Finite Commutative Rings", International Journalof Computer Applications,vol. 13 pp. 38-42, 2011.
  • [5]. P.W. Chen, A kind of graph structure of rings, Algebra Colloq.,vol. 10 (2),pp. 229-238, 2003.
  • [6]. S. Akbari, A. Mohammadian, "Zero-divisor graphs of non-commutative rings", J. Algebra, vol. 296, pp. 462-479, 2006.
  • [7]. S.Akbari, A. Mohammadian, "On zero-divisor graphs of finite rings", J. Algebra, vol. 13, pp. 168-184, 2007.
  • [8]. S. J. Kirkland, "Completion of Laplacian integral graphs via edge additions", Discrete Math, vol. 295,pp. 75-90, 2005.

Laplacian spectral properties of nilpotent graphs over ring Z_n

Year 2017, Volume: 21 Issue: 6, 1443 - 1447, 01.12.2017

Sezer Sorgun Hatice Pınar Cantekin

https://doi.org/10.16984/saufenbilder.277822

Abstract

We
consider a
ring  with unity. The
nilpotent graph of  is a graph with
vertex set ; and two distinct vertices  and  are adjacent iff , where  is the set of all
nilpotent elements of  and it is denoted by. In this paper we study Laplacian spectral properties of
the nilpotent graph over the ring .

Keywords

Nilpotent Graph Laplacian matrix Spectrum

References

  • [1]. D.F. Anderson, P.S. Livingston, "The zero-divisor graph of a commutative ring", J. Algebra, vol. 217, pp. 434-447, 1999.
  • [2]. D.F. Anderson, A. Badawi, "The total graph of a commutative ring", J. Algebra, vol. 320, pp. 2706-2719, 2008.
  • [3]. M.J.Nikmehr, S.Khojasteh, "On the nilpotent graph of a ring", Turkish Journal of Mathematics, vol. 37, pp. 553-559, 2013.
  • [4]. P. Sharma, A.Sharma, R.K. Vats, "Analysis of Adjacency Matrix and Neighborhood Associated with Zero Divisor Graph of Finite Commutative Rings", International Journalof Computer Applications,vol. 13 pp. 38-42, 2011.
  • [5]. P.W. Chen, A kind of graph structure of rings, Algebra Colloq.,vol. 10 (2),pp. 229-238, 2003.
  • [6]. S. Akbari, A. Mohammadian, "Zero-divisor graphs of non-commutative rings", J. Algebra, vol. 296, pp. 462-479, 2006.
  • [7]. S.Akbari, A. Mohammadian, "On zero-divisor graphs of finite rings", J. Algebra, vol. 13, pp. 168-184, 2007.
  • [8]. S. J. Kirkland, "Completion of Laplacian integral graphs via edge additions", Discrete Math, vol. 295,pp. 75-90, 2005.
There are 8 citations in total.

Details

Subjects Engineering
Journal Section Research Articles
Authors

Sezer Sorgun

Hatice Pınar Cantekin

Publication Date December 1, 2017
Submission Date December 14, 2016
Acceptance Date September 12, 2017
Published in Issue Year 2017 Volume: 21 Issue: 6

Cite

APA Sorgun, S., & Cantekin, H. P. (2017). Laplacian spectral properties of nilpotent graphs over ring Z_n. Sakarya University Journal of Science, 21(6), 1443-1447. https://doi.org/10.16984/saufenbilder.277822
AMA Sorgun S, Cantekin HP. Laplacian spectral properties of nilpotent graphs over ring Z_n. SAUJS. December 2017;21(6):1443-1447. doi:10.16984/saufenbilder.277822
Chicago Sorgun, Sezer, and Hatice Pınar Cantekin. “Laplacian Spectral Properties of Nilpotent Graphs over Ring Z_n”. Sakarya University Journal of Science 21, no. 6 (December 2017): 1443-47. https://doi.org/10.16984/saufenbilder.277822.
EndNote Sorgun S, Cantekin HP (December 1, 2017) Laplacian spectral properties of nilpotent graphs over ring Z_n. Sakarya University Journal of Science 21 6 1443–1447.
IEEE S. Sorgun and H. P. Cantekin, “Laplacian spectral properties of nilpotent graphs over ring Z_n”, SAUJS, vol. 21, no. 6, pp. 1443–1447, 2017, doi: 10.16984/saufenbilder.277822.
ISNAD Sorgun, Sezer - Cantekin, Hatice Pınar. “Laplacian Spectral Properties of Nilpotent Graphs over Ring Z_n”. Sakarya University Journal of Science 21/6 (December 2017), 1443-1447. https://doi.org/10.16984/saufenbilder.277822.
JAMA Sorgun S, Cantekin HP. Laplacian spectral properties of nilpotent graphs over ring Z_n. SAUJS. 2017;21:1443–1447.
MLA Sorgun, Sezer and Hatice Pınar Cantekin. “Laplacian Spectral Properties of Nilpotent Graphs over Ring Z_n”. Sakarya University Journal of Science, vol. 21, no. 6, 2017, pp. 1443-7, doi:10.16984/saufenbilder.277822.
Vancouver Sorgun S, Cantekin HP. Laplacian spectral properties of nilpotent graphs over ring Z_n. SAUJS. 2017;21(6):1443-7.
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