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Devirli Grupların Power Graflarının Enerjileri İçin Bazı Sınırlar

Yıl 2023, Cilt: 23 Sayı: 6, 1412 - 1417, 28.12.2023

Nurşah Mutlu Varlıoğlu Şerife Büyükköse

https://doi.org/10.35414/akufemubid.1259571

Öz

Bu çalışmada, sonlu bir devirli grubun power grafının komşuluk matrisi yapısı dikkate alınarak, sonlu devirli grupların power graflarının enerjileri için bazı alt ve üst sınırlar elde edilmiştir. Daha sonra devirli bir grubun mertebesinin bir asal sayının pozitif tam sayı kuvveti olması durumu ile bu devirli gruba karşılık gelen power grafın tamlığı arasındaki ilişki kullanılarak bazı sonuçlar verilmiştir.

Anahtar Kelimeler

Devirli grup Power graf Enerji Sınır

Kaynakça

  • Abreu, N.M.M., Gutman, I., Robbiano, M. and So, W., 2010. Applications of a theorem by Ky Fan in the theory of graph energy. Linear Algebra and its Applications, 432, 2163-2169.
  • Cameron, P.J., 2010. The power graph of a finite group ll. Journal of Group Theory 13, 779-783.
  • Cameron, P.J. and Ghosh, S., 2011. The power graph of a finite group. Discrete Mathematics, 311(3), 1220-1222.
  • Cavers, M., Fallat, S., Kirkland, S., 2010. On the normalized laplacian energy and general Randi'c index R₋₁ of graphs. Linear Algebra and its Applications, 443, 172-190.
  • Chakrabarty, I., Ghosh, S., Sen, M.K., 2009. Undirected Power Graphs of Semigroups. Semigroup Forum, 78, 410-426.
  • Chattopadhyay, S., Panigrahi, P., 2014. Connectivity and planarity of power graphs of finite cylclic, dihedral and dicyclic groups. Algebra and Discrete Mathematics, 18, 42-49.
  • Chattopadhyay, S., Panigrahi, P., 2015. Some relations between power graphs and Cayley graphs. Journal of the Egyptian Mathematical Society, 23, 457-462.
  • Chattopadhyay, S., Panigrahi, P. and Atik, F., 2018. Spectral radius of power graphs on certain finite groups, Indagationes Mathematicae, 29, 730-737.
  • Gutman, I., 1978. The energy of graph. 10. Steirmarkisches Mathematisches Symposium, 103, 1-22.
  • Gutman, I. and Zhou, B., 2006. Laplacian energy of a graph. Linear Algebra and its Applications, 414, 29-37.
  • Gutman, I., Indulal, G. and Vijayakumar, A., 2008. On distance energy of graphs. MATCH Communications in Mathematical and Computer Chemistry, 60, 461-472.
  • Horn, R.A. and Johnson, C.R., 2012. Matrix Analysis. 2 nd edition, Cambridge/United Kingdom: Cambridge University Press, 42.
  • Hwang, S.G., 2004. Cauchy's interlace theorem for eigenvalues of hermitian matrices. The American Mathematical Monthly, 111, 157-159.
  • Kelarev, A.V. and Quinn, S.J., 2002. Directed graphs and combinatorial properties of semigroups. Journal of Algebra, 251(1), 16-26.
  • Kelarev, A.V. and Quinn, S.J., 2004. A combinatorial property and power graphs of semigroups. Commentationes Mathematicae Universitatis Carolinae, 45(1), 1-7.
  • Kelarev, A.V. and Quinn, S.J., 2000. A combinatorial property and power graphs of groups. Contributions to General Algebra, 12, 229-235.
  • Lütkepohl, H., 1996. Handbook of matrices. First edition, Chichester: John Wiley & Sons, 268, 280.
  • Oboudi, M.R., 2019. A new lower bound for the energy of graphs. Linear Algebra and its Applications, 580, 384-395.

Some Bounds for The Energies of The Power Graphs of Cyclic Groups

Yıl 2023, Cilt: 23 Sayı: 6, 1412 - 1417, 28.12.2023

Nurşah Mutlu Varlıoğlu Şerife Büyükköse

https://doi.org/10.35414/akufemubid.1259571

Öz

In this study, some lower and upper bounds were obtained for the energies of the power graphs of finite cyclic groups by considering the adjacency matrix structure of the power graph of a finite cyclic group. Then, some results are given using the relationship between the case where the order of a cyclic group is the positive integer power of a prime number and the completeness of the power graph corresponding to this cyclic group.

Anahtar Kelimeler

Cyclic group Power graph Energy Bound

Kaynakça

  • Abreu, N.M.M., Gutman, I., Robbiano, M. and So, W., 2010. Applications of a theorem by Ky Fan in the theory of graph energy. Linear Algebra and its Applications, 432, 2163-2169.
  • Cameron, P.J., 2010. The power graph of a finite group ll. Journal of Group Theory 13, 779-783.
  • Cameron, P.J. and Ghosh, S., 2011. The power graph of a finite group. Discrete Mathematics, 311(3), 1220-1222.
  • Cavers, M., Fallat, S., Kirkland, S., 2010. On the normalized laplacian energy and general Randi'c index R₋₁ of graphs. Linear Algebra and its Applications, 443, 172-190.
  • Chakrabarty, I., Ghosh, S., Sen, M.K., 2009. Undirected Power Graphs of Semigroups. Semigroup Forum, 78, 410-426.
  • Chattopadhyay, S., Panigrahi, P., 2014. Connectivity and planarity of power graphs of finite cylclic, dihedral and dicyclic groups. Algebra and Discrete Mathematics, 18, 42-49.
  • Chattopadhyay, S., Panigrahi, P., 2015. Some relations between power graphs and Cayley graphs. Journal of the Egyptian Mathematical Society, 23, 457-462.
  • Chattopadhyay, S., Panigrahi, P. and Atik, F., 2018. Spectral radius of power graphs on certain finite groups, Indagationes Mathematicae, 29, 730-737.
  • Gutman, I., 1978. The energy of graph. 10. Steirmarkisches Mathematisches Symposium, 103, 1-22.
  • Gutman, I. and Zhou, B., 2006. Laplacian energy of a graph. Linear Algebra and its Applications, 414, 29-37.
  • Gutman, I., Indulal, G. and Vijayakumar, A., 2008. On distance energy of graphs. MATCH Communications in Mathematical and Computer Chemistry, 60, 461-472.
  • Horn, R.A. and Johnson, C.R., 2012. Matrix Analysis. 2 nd edition, Cambridge/United Kingdom: Cambridge University Press, 42.
  • Hwang, S.G., 2004. Cauchy's interlace theorem for eigenvalues of hermitian matrices. The American Mathematical Monthly, 111, 157-159.
  • Kelarev, A.V. and Quinn, S.J., 2002. Directed graphs and combinatorial properties of semigroups. Journal of Algebra, 251(1), 16-26.
  • Kelarev, A.V. and Quinn, S.J., 2004. A combinatorial property and power graphs of semigroups. Commentationes Mathematicae Universitatis Carolinae, 45(1), 1-7.
  • Kelarev, A.V. and Quinn, S.J., 2000. A combinatorial property and power graphs of groups. Contributions to General Algebra, 12, 229-235.
  • Lütkepohl, H., 1996. Handbook of matrices. First edition, Chichester: John Wiley & Sons, 268, 280.
  • Oboudi, M.R., 2019. A new lower bound for the energy of graphs. Linear Algebra and its Applications, 580, 384-395.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Nurşah Mutlu Varlıoğlu 0000-0003-0873-6277

Şerife Büyükköse 0000-0001-7629-4277

Erken Görünüm Tarihi 22 Aralık 2023
Yayımlanma Tarihi 28 Aralık 2023
Gönderilme Tarihi 3 Mart 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 23 Sayı: 6

Kaynak Göster

APA Mutlu Varlıoğlu, N., & Büyükköse, Ş. (2023). Some Bounds for The Energies of The Power Graphs of Cyclic Groups. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 23(6), 1412-1417. https://doi.org/10.35414/akufemubid.1259571
AMA Mutlu Varlıoğlu N, Büyükköse Ş. Some Bounds for The Energies of The Power Graphs of Cyclic Groups. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. Aralık 2023;23(6):1412-1417. doi:10.35414/akufemubid.1259571
Chicago Mutlu Varlıoğlu, Nurşah, ve Şerife Büyükköse. “Some Bounds for The Energies of The Power Graphs of Cyclic Groups”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 23, sy. 6 (Aralık 2023): 1412-17. https://doi.org/10.35414/akufemubid.1259571.
EndNote Mutlu Varlıoğlu N, Büyükköse Ş (01 Aralık 2023) Some Bounds for The Energies of The Power Graphs of Cyclic Groups. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 23 6 1412–1417.
IEEE N. Mutlu Varlıoğlu ve Ş. Büyükköse, “Some Bounds for The Energies of The Power Graphs of Cyclic Groups”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 23, sy. 6, ss. 1412–1417, 2023, doi: 10.35414/akufemubid.1259571.
ISNAD Mutlu Varlıoğlu, Nurşah - Büyükköse, Şerife. “Some Bounds for The Energies of The Power Graphs of Cyclic Groups”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 23/6 (Aralık 2023), 1412-1417. https://doi.org/10.35414/akufemubid.1259571.
JAMA Mutlu Varlıoğlu N, Büyükköse Ş. Some Bounds for The Energies of The Power Graphs of Cyclic Groups. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2023;23:1412–1417.
MLA Mutlu Varlıoğlu, Nurşah ve Şerife Büyükköse. “Some Bounds for The Energies of The Power Graphs of Cyclic Groups”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 23, sy. 6, 2023, ss. 1412-7, doi:10.35414/akufemubid.1259571.
Vancouver Mutlu Varlıoğlu N, Büyükköse Ş. Some Bounds for The Energies of The Power Graphs of Cyclic Groups. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2023;23(6):1412-7.
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