Energy of commuting graph of finite AC- groups

Reza Sharafdini; Rajat Kanti Nath; Rezvan Darbandi

Ayuda

Energy of commuting graph of finite AC- groups

Sharafdini, Reza ^[1] ; Nath, Rajat Kanti ^[2] ; Darbandi, Rezvan ^[3]
1. [1] Persian Gulf University
  
  Persian Gulf University
  
  Irán
2. [2] Tezpur University
  
  Tezpur University
  
  India
3. [3] Amirkabir University of Technology
  
  Amirkabir University of Technology
  
  Irán
Mostrar afiliaciones +
Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 1, 2022, págs. 263-273
Idioma: inglés
DOI: 10.22199/issn.0717-6279-4365
Enlaces
- Texto completo
Resumen
- Let Γ be a graph with the adjacency matrix A. The energy of Γ is the sum of the absolute values of the eigenvalues of A. In this article we compute the energies of the commuting graphs of some finite groups and discuss some consequences regarding hyperenergetic and borderenergetic graphs.
Referencias bibliográficas
- A. Abdollahi, S. Akbari, and H. R. Maimani, “Non-commuting graph of a group”, Journal of algebra, vol. 298, no. 2, pp. 468–492, 2006. https://doi.org/10.1016/j.jalgebra.2006.02.015
- A. R. Ashrafi, “On finite groups with a given number of centralizers”, Algebra colloquium, vol. 7, no. 2, pp. 139–146, 2000. https://doi.org/10.1007/s10011-000-0139-5
- S. Akbari, A. Mohammadian, H. Radjavi, and P. Raja, “On the diameters of commuting graphs”, Linear algebra and its applications, vol. 418,...
- C. Bates, D. Bundy, S. Hart, and P. Rowley, “A note on commuting graphs for symmetric groups”, The electronic journal of combinatorics, vol....
- S. M. Belcastro and G. J. Sherman, “Counting centralizers in finite groups”, Mathematics magazine, vol. 67, no. 5, pp. 366–374, 1994. https://doi.org/10.1080/0025570x.1994.11996252
- J. Dutta and R. K. Nath, “Spectrum of commuting graphs of some classes of finite groups”, Matematika, vol. 33, no. 1, p. 87, 2017. https://doi.org/10.11113/matematika.v33.n1.812
- J. Dutta and R. K. Nath, “Finite groups whose commuting graphs are integral”, Matematicki vesnik, vol. 69, no. 3, pp. 226-230, 2017. [On line]....
- J. Dutta and R. K. Nath, “Laplacian and signless Laplacian spectrum of commuting graphs of finite groups”, Khayyam journal of mathematics,...
- P. Dutta, J. Dutta, and R. K. Nath, “Laplacian spectrum of non-commuting graphs of finite groups”, Indian journal of pure and applied mathematics,...
- P. Dutta and R. K. Nath, “On Laplacian energy of non-commuting graphs of finite groups”, Journal of linear and topological algebra, vol. 7,...
- S. C. Gong, X. Li, G. H. Xu, I. Gutman and B. Furtula, “Borderenergetic graphs”, MATCH communications in mathematical and in computer chemistry,...
- I. Gutman, “The energy of a graph”, Berichte der Mathematisch-statistischen Sektion im Forschungszentrum Graz, vol. 103, pp. 1-22, 1978.
- I. Gutman, “Hyperenergetic molecular graphs”, Journal of the serbian chemical society, vol. 64, pp. 199-205, 1999.
- X. Li, Y. Shi, I. Gutman, Graph energy, New York: Springer, 2012.
- A. Iranmanesh and A. Jafarzadeh, “Characterization of finite groups by their commuting graph”, Acta mathematica academiae paedagogiace nyíregyháziensis,...
- A. Iranmanesh and A. Jafarzadeh, “On the commuting graph associated with the symmetric and alternating groups”, Journal of algebra and its...
- G. L. Morgan and C. W. Parker, “The diameter of the commuting graph of a finite group with Trivial Centre”, Journal of algebra, vol. 393,...
- R. K. Nath, “Various spectra of commuting graphs of N-centralizer finite groups”, International Journal of Engineering Science and Technology,...
- B. H. Neumann, “A problem of Paul Erdös on groups”, Journal of the Australian mathematical society, vol. 21, no. 4, pp. 467–472, 1976. https://doi.org/10.1017/s1446788700019303
- C. Parker, “The commuting graph of a soluble group”, Bulletin of the London mathematical society, vol. 45, no. 4, pp. 839–848, 2013. https://doi.org/10.1112/blms/bdt005
- H. B. Walikar, H. S. Ramane and P. R. Hampiholi, “On the energy of agraph”, in Graph Connections, R. Balakrishnan, H. M. Mulder and A. Vijayakumar,...