Araştırma Makalesi
BibTex RIS Kaynak Göster

On analogues of nilpotent and total graphs associated ring $\mathbb{Z}_n$

Yıl 2023, Cilt: 2 Sayı: 1, 1 - 4, 30.06.2023

Öz

In the last 20 years, the graphs associated with a ring have been introduced, such as the zero-divisor graph, the nilpotent graph, the total graph, etc. The studies on these graphs are generally related to their graph invariants. In this paper, we define two novel analogue graphs over the integer rings and obtain some properties as well as the spectrum with respect to the adjacency matrix.

Kaynakça

  • Anderson, D. F., Livingston, P. S. (1999). The zero-divisor graph of a commutative ring. Journal of Algebra, 217, 434-447.
  • Anderson, D. F., Levy, R., Shapiro, J. (2003). Zero-divisor graphs, von Neumann regular rings and Boolean algebras. J. Pure Appl. Algebra, 180, 221- 241.
  • Anderson, D. F., Badawi, A. (2008). The total graph of a commutative ring. Journal of Algebra, 320, 2706-2719.
  • Anderson, D. F., Asir, T., Badawi,A., Chelvam, T.T. (2021). Graphs from rings. Springer.
  • Brouwer, A. E., Haemers, W. H. (2012). Spectra of graphs. Springer.
  • Bajaj, S., Panigrahi, P. (2022). On the adjacency spectrum of zero divisor graph of ring Zn. Journal of Algebra and its Appl., 21 (10), 2250197. Cantekin, H. P. Sorgun, S. (2017). Laplacian spectral properties of nilpotent graphs over the ring Z_n. Sakarya University Journal of Science, 21 (6), 1443-1447.
  • Chattopadhyay, S., Patra, K.L., Sahoo, B.K. (2020). Laplacian eigenvalues of the zero divisor graph of the ring Zn. Linear Algebra and its Appl, 584, 267-286.
  • Li, A. H., Li, Q. S. (2010). A kind of graph structure on von-Neumann regular rings. International Journal of Algebra, 4, 291-302.
  • Nikmehr, M.J., Khojasteh, S. (2013). On the nilpotent graph of a ring. Turkish Journal of Mathematics, 37, 553-559.
  • Pirzada ,S. Rather B. A. , Aijaz, M., Chishti, T. A. (2022). On distance signless Laplacian spectrum of graphs and spectrum of zero divisor graphs of Z_n. Linear and Multilinear Algebra, 70 (17), 3354-3369.
  • Pirzada, S., Rather, B., Shaban, R., Chishti, T. (2023). Signless Laplacian eigenvalues of the zero divisor graph associated to finite commutative ring. Communications in Comb. and Opt., 8 (3), 561-574.
  • Singh, P., Bhat, K.V. (2020). Zero-divisor graphs of finite commutative rings :a survey. Surveys in Mathematics and its Applications, 15, 371-397.

$\mathbb{Z}_n$ halkası üzerinde tanımlı nilpotent ve total grafların analogları üzerine

Yıl 2023, Cilt: 2 Sayı: 1, 1 - 4, 30.06.2023

Öz

Son 20 yıldır, sıfır bölen çizge, nilpotent çizge ve total çizge gibi bir halkadan oluşmuş çizgeler tanıtılmıştır. Bu çizgeler üzerinde yapılan çalışmalar genellikle .çizge değişmezleri üzerinedir. Bu makalede nilpotent ve total çizgelerden yardımıyla Z_n tam sayı halkasında iki yeni benzer çizge tanımı yapılmıştır ve bu çizgelerin komşuluk spektrumları yanı sıra bazı özellikleri der verilmiştir.

Kaynakça

  • Anderson, D. F., Livingston, P. S. (1999). The zero-divisor graph of a commutative ring. Journal of Algebra, 217, 434-447.
  • Anderson, D. F., Levy, R., Shapiro, J. (2003). Zero-divisor graphs, von Neumann regular rings and Boolean algebras. J. Pure Appl. Algebra, 180, 221- 241.
  • Anderson, D. F., Badawi, A. (2008). The total graph of a commutative ring. Journal of Algebra, 320, 2706-2719.
  • Anderson, D. F., Asir, T., Badawi,A., Chelvam, T.T. (2021). Graphs from rings. Springer.
  • Brouwer, A. E., Haemers, W. H. (2012). Spectra of graphs. Springer.
  • Bajaj, S., Panigrahi, P. (2022). On the adjacency spectrum of zero divisor graph of ring Zn. Journal of Algebra and its Appl., 21 (10), 2250197. Cantekin, H. P. Sorgun, S. (2017). Laplacian spectral properties of nilpotent graphs over the ring Z_n. Sakarya University Journal of Science, 21 (6), 1443-1447.
  • Chattopadhyay, S., Patra, K.L., Sahoo, B.K. (2020). Laplacian eigenvalues of the zero divisor graph of the ring Zn. Linear Algebra and its Appl, 584, 267-286.
  • Li, A. H., Li, Q. S. (2010). A kind of graph structure on von-Neumann regular rings. International Journal of Algebra, 4, 291-302.
  • Nikmehr, M.J., Khojasteh, S. (2013). On the nilpotent graph of a ring. Turkish Journal of Mathematics, 37, 553-559.
  • Pirzada ,S. Rather B. A. , Aijaz, M., Chishti, T. A. (2022). On distance signless Laplacian spectrum of graphs and spectrum of zero divisor graphs of Z_n. Linear and Multilinear Algebra, 70 (17), 3354-3369.
  • Pirzada, S., Rather, B., Shaban, R., Chishti, T. (2023). Signless Laplacian eigenvalues of the zero divisor graph associated to finite commutative ring. Communications in Comb. and Opt., 8 (3), 561-574.
  • Singh, P., Bhat, K.V. (2020). Zero-divisor graphs of finite commutative rings :a survey. Surveys in Mathematics and its Applications, 15, 371-397.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematiksel Fizik
Bölüm Araştırma Makaleleri
Yazarlar

Hatice Pınar Cantekin 0000-0002-9692-275X

Sezer Sorgun 0000-0001-8708-1226

Erken Görünüm Tarihi 16 Haziran 2023
Yayımlanma Tarihi 30 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 2 Sayı: 1

Kaynak Göster

APA Cantekin, H. P., & Sorgun, S. (2023). On analogues of nilpotent and total graphs associated ring $\mathbb{Z}_n$. Sivas Cumhuriyet Üniversitesi Bilim Ve Teknoloji Dergisi, 2(1), 1-4.
AMA Cantekin HP, Sorgun S. On analogues of nilpotent and total graphs associated ring $\mathbb{Z}_n$. CUJAST. Haziran 2023;2(1):1-4.
Chicago Cantekin, Hatice Pınar, ve Sezer Sorgun. “On Analogues of Nilpotent and Total Graphs Associated Ring $\mathbb{Z}_n$”. Sivas Cumhuriyet Üniversitesi Bilim Ve Teknoloji Dergisi 2, sy. 1 (Haziran 2023): 1-4.
EndNote Cantekin HP, Sorgun S (01 Haziran 2023) On analogues of nilpotent and total graphs associated ring $\mathbb{Z}_n$. Sivas Cumhuriyet Üniversitesi Bilim ve Teknoloji Dergisi 2 1 1–4.
IEEE H. P. Cantekin ve S. Sorgun, “On analogues of nilpotent and total graphs associated ring $\mathbb{Z}_n$”, CUJAST, c. 2, sy. 1, ss. 1–4, 2023.
ISNAD Cantekin, Hatice Pınar - Sorgun, Sezer. “On Analogues of Nilpotent and Total Graphs Associated Ring $\mathbb{Z}_n$”. Sivas Cumhuriyet Üniversitesi Bilim ve Teknoloji Dergisi 2/1 (Haziran 2023), 1-4.
JAMA Cantekin HP, Sorgun S. On analogues of nilpotent and total graphs associated ring $\mathbb{Z}_n$. CUJAST. 2023;2:1–4.
MLA Cantekin, Hatice Pınar ve Sezer Sorgun. “On Analogues of Nilpotent and Total Graphs Associated Ring $\mathbb{Z}_n$”. Sivas Cumhuriyet Üniversitesi Bilim Ve Teknoloji Dergisi, c. 2, sy. 1, 2023, ss. 1-4.
Vancouver Cantekin HP, Sorgun S. On analogues of nilpotent and total graphs associated ring $\mathbb{Z}_n$. CUJAST. 2023;2(1):1-4.