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On Cayley Graphs with Constant Ricci Curvature

Yıl 2024, Cilt: 16 Sayı: 1, 255 - 260, 30.06.2024
https://doi.org/10.47000/tjmcs.1492247

Öz

Understanding the geometry of graphs has become increasingly important. One approach utilizes the Ricci curvature introduced by Lin, Lu, and Yau, which offers a valuable isomorphism invariant for locally finite graphs. One of the key tools used in calculating curvatures is the matching condition. This paper exploits the matching condition to construct families of Cayley graphs exhibiting constant Ricci curvature.

Kaynakça

  • Bauer, F., Jost, J., Liu, L., Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator, Math. Res. Lett., 19(6)(2012), 1185–1205.
  • Bhattacharya, B.B., Mukherjee, S., Exact and asymptotic results on coarse Ricci curvature of graphs, Discrete Math., 338(1)(2015), 23–42.
  • Cushing, D., Kamtue, S., Kangaslampi, R., Liu, S., Münch, F. et al., Bakry-E´mery and Ollivier Ricci curvature of Cayley graphs, arXiv:2310.15953, (2023).
  • Dağlı, M., Olmez, O., Smith, J.D.H., Ricci curvature, circulants, and extended matching conditions, B. Korean Math. Soc., 56(1)(2019), 201–217.
  • Eidi, M., Jost, J., Ollivier Ricci curvature of directed hypergraphs, Scientific Reports, 10(2020).
  • Li, H., Cao, J., Zhu, J., Liu, Y., Zhu, Q. et al. Curvature graph neural network, Information Sciences, 592(2022), 50–66.
  • Lin, Y., Lu, L., Yau, S. T., Ricci curvature of graphs, Tohoku Math. J., 63(4)(2011), 605–627.
  • Mizukai, I., Akifumi Sako, Ricci curvature of Cayley graphs for dihedral groups, generalized quaternion groups, and cyclic groups, arXiv:2210.00860v4, (2024).
  • Ni, C.-C., Lin, Y.-Y., Gao, J., X. Gu, D. X., Saucan, E., Ricci curvature of the internet topology, IEEE Conference on Computer Communications (INFOCOM), Hong Kong, China (2015), 2758–2766.
  • Ollivier, Y., Ricci curvature of Markov chains on metric spaces, Journal of Functional Analysis, 256(3)(2009), 810–864.
  • Ollivier, Y., A survey of Ricci curvature for metric spaces and Markov chains, Advanced Studies in Pure Mathematics, 57(2010).
  • Sandhu, R.S., Georgiou, T.T., Reznik, E., Zhu, L., Kolesov, I. et al., Graph curvature for differentiating cancer networks, Scientific Reports, 5(2015).
  • Sandhu, R.S., Georgiou, T.T., Tannenbaum, A.R., Ricci curvature: An economic indicator for market fragility and systemic risk, Science Advances, 2(5)(2016).
  • Smith, J.D.H., Ricci curvature, circulants, and a matching condition, Discrete Mathematics, 329(2014), 88–98.
  • Ünver, Y., Cayley graphs with constant Ricci curvature, Master’s Thesis, Amasya University, 2022.
Yıl 2024, Cilt: 16 Sayı: 1, 255 - 260, 30.06.2024
https://doi.org/10.47000/tjmcs.1492247

Öz

Kaynakça

  • Bauer, F., Jost, J., Liu, L., Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator, Math. Res. Lett., 19(6)(2012), 1185–1205.
  • Bhattacharya, B.B., Mukherjee, S., Exact and asymptotic results on coarse Ricci curvature of graphs, Discrete Math., 338(1)(2015), 23–42.
  • Cushing, D., Kamtue, S., Kangaslampi, R., Liu, S., Münch, F. et al., Bakry-E´mery and Ollivier Ricci curvature of Cayley graphs, arXiv:2310.15953, (2023).
  • Dağlı, M., Olmez, O., Smith, J.D.H., Ricci curvature, circulants, and extended matching conditions, B. Korean Math. Soc., 56(1)(2019), 201–217.
  • Eidi, M., Jost, J., Ollivier Ricci curvature of directed hypergraphs, Scientific Reports, 10(2020).
  • Li, H., Cao, J., Zhu, J., Liu, Y., Zhu, Q. et al. Curvature graph neural network, Information Sciences, 592(2022), 50–66.
  • Lin, Y., Lu, L., Yau, S. T., Ricci curvature of graphs, Tohoku Math. J., 63(4)(2011), 605–627.
  • Mizukai, I., Akifumi Sako, Ricci curvature of Cayley graphs for dihedral groups, generalized quaternion groups, and cyclic groups, arXiv:2210.00860v4, (2024).
  • Ni, C.-C., Lin, Y.-Y., Gao, J., X. Gu, D. X., Saucan, E., Ricci curvature of the internet topology, IEEE Conference on Computer Communications (INFOCOM), Hong Kong, China (2015), 2758–2766.
  • Ollivier, Y., Ricci curvature of Markov chains on metric spaces, Journal of Functional Analysis, 256(3)(2009), 810–864.
  • Ollivier, Y., A survey of Ricci curvature for metric spaces and Markov chains, Advanced Studies in Pure Mathematics, 57(2010).
  • Sandhu, R.S., Georgiou, T.T., Reznik, E., Zhu, L., Kolesov, I. et al., Graph curvature for differentiating cancer networks, Scientific Reports, 5(2015).
  • Sandhu, R.S., Georgiou, T.T., Tannenbaum, A.R., Ricci curvature: An economic indicator for market fragility and systemic risk, Science Advances, 2(5)(2016).
  • Smith, J.D.H., Ricci curvature, circulants, and a matching condition, Discrete Mathematics, 329(2014), 88–98.
  • Ünver, Y., Cayley graphs with constant Ricci curvature, Master’s Thesis, Amasya University, 2022.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Kombinatorik ve Ayrık Matematik (Fiziksel Kombinatorik Hariç)
Bölüm Makaleler
Yazarlar

Mehmet Dağlı 0000-0003-0215-5711

Yonca Ünver Bu kişi benim 0000-0001-8875-5667

Yayımlanma Tarihi 30 Haziran 2024
Gönderilme Tarihi 29 Mayıs 2024
Kabul Tarihi 25 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 16 Sayı: 1

Kaynak Göster

APA Dağlı, M., & Ünver, Y. (2024). On Cayley Graphs with Constant Ricci Curvature. Turkish Journal of Mathematics and Computer Science, 16(1), 255-260. https://doi.org/10.47000/tjmcs.1492247
AMA Dağlı M, Ünver Y. On Cayley Graphs with Constant Ricci Curvature. TJMCS. Haziran 2024;16(1):255-260. doi:10.47000/tjmcs.1492247
Chicago Dağlı, Mehmet, ve Yonca Ünver. “On Cayley Graphs With Constant Ricci Curvature”. Turkish Journal of Mathematics and Computer Science 16, sy. 1 (Haziran 2024): 255-60. https://doi.org/10.47000/tjmcs.1492247.
EndNote Dağlı M, Ünver Y (01 Haziran 2024) On Cayley Graphs with Constant Ricci Curvature. Turkish Journal of Mathematics and Computer Science 16 1 255–260.
IEEE M. Dağlı ve Y. Ünver, “On Cayley Graphs with Constant Ricci Curvature”, TJMCS, c. 16, sy. 1, ss. 255–260, 2024, doi: 10.47000/tjmcs.1492247.
ISNAD Dağlı, Mehmet - Ünver, Yonca. “On Cayley Graphs With Constant Ricci Curvature”. Turkish Journal of Mathematics and Computer Science 16/1 (Haziran 2024), 255-260. https://doi.org/10.47000/tjmcs.1492247.
JAMA Dağlı M, Ünver Y. On Cayley Graphs with Constant Ricci Curvature. TJMCS. 2024;16:255–260.
MLA Dağlı, Mehmet ve Yonca Ünver. “On Cayley Graphs With Constant Ricci Curvature”. Turkish Journal of Mathematics and Computer Science, c. 16, sy. 1, 2024, ss. 255-60, doi:10.47000/tjmcs.1492247.
Vancouver Dağlı M, Ünver Y. On Cayley Graphs with Constant Ricci Curvature. TJMCS. 2024;16(1):255-60.