Araştırma Makalesi
BibTex RIS Kaynak Göster

Z_n Halkası üzerinde nilpotent grafların laplasyan spektral özellikleri

Yıl 2017, Cilt: 21 Sayı: 6, 1443 - 1447, 01.12.2017

Sezer Sorgun Hatice Pınar Cantekin

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

Öz

 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.

Anahtar Kelimeler

Nilpotent graph Laplasyan Spektrum

Kaynakça

  • [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

Yıl 2017, Cilt: 21 Sayı: 6, 1443 - 1447, 01.12.2017

Sezer Sorgun Hatice Pınar Cantekin

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

Öz

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 .

Anahtar Kelimeler

Nilpotent Graph Laplacian matrix Spectrum

Kaynakça

  • [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.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Sezer Sorgun

Hatice Pınar Cantekin

Yayımlanma Tarihi 1 Aralık 2017
Gönderilme Tarihi 14 Aralık 2016
Kabul Tarihi 12 Eylül 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 21 Sayı: 6

Kaynak Göster

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. Aralık 2017;21(6):1443-1447. doi:10.16984/saufenbilder.277822
Chicago Sorgun, Sezer, ve Hatice Pınar Cantekin. “Laplacian Spectral Properties of Nilpotent Graphs over Ring Z_n”. Sakarya University Journal of Science 21, sy. 6 (Aralık 2017): 1443-47. https://doi.org/10.16984/saufenbilder.277822.
EndNote Sorgun S, Cantekin HP (01 Aralık 2017) Laplacian spectral properties of nilpotent graphs over ring Z_n. Sakarya University Journal of Science 21 6 1443–1447.
IEEE S. Sorgun ve H. P. Cantekin, “Laplacian spectral properties of nilpotent graphs over ring Z_n”, SAUJS, c. 21, sy. 6, ss. 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 (Aralık 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 ve Hatice Pınar Cantekin. “Laplacian Spectral Properties of Nilpotent Graphs over Ring Z_n”. Sakarya University Journal of Science, c. 21, sy. 6, 2017, ss. 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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