Spectrum and energies of commuting conjugacy class graph of a finite group

Document Type : Research Paper

Authors

1 Department of Mathematics, Cachar College, Silchar-788001, Assam, India.

2 Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, As sam, India.

Abstract

In this paper we compute spectrum, Laplacian spectrum, signless Laplacian spectrum and their corresponding energies of commuting conjugacy class graph of the group G(p,m,n)=⟨x,y:xpm=ypn=[x,y]p=1,[x,[x,y]]=[y,[x,y]]=1⟩, where p is any prime, m≥1 and n≥1. We derive some consequences along with the fact that commuting conjugacy class graph of G(p,m,n) is super integral. We also compare various energies and determine whether commuting conjugacy class graph of G(p,m,n) is hyperenergetic, L-hyperenergetic or Q-hyperenergetic.

Keywords

References

[1] P. Bhowal and R. K. Nath, Spectral aspects of commuting conjugacy class graph of finite groups, Alg. Struc. Appl., 8 No. 2 (2021) 67-118.
[2] P. Bhowal and R. K. Nath, Genus of commuting conjugacy class graph of certain finite groups, Alg. Struc. Appl., 9 No. 1 (2022) 93-108.
[3] R. Brauer and K. A. Fowler, On groups of even order, Ann. of Math., 62 No. 2 (1955) 565-583.
[4] P. Dutta, B. Bagchi and R. K. Nath, Various energies of commuting graphs of finite nonabelian groups, Khayyam J. Math., 6 No. 1 (2020) 27-45.
[5] J. Dutta and R. K. Nath, Laplacian and signless Laplacian spectrum of commuting graphs of finite groups, Khayyam J. Math., 4 No. 1 (2018) 77-87.
[6] W. N. T. Fasfous, R. K. Nath and R. Sharafdini, Various spectra and energies of commuting graphs of finite rings, Hacet. J. Math. Stat., 49 No. 6 (2020) 1915-1925.
[7] S. C. Gong, X. Li, G. H. Xu, I. Gutman and B. Furtula, Borderenergetic graphs, MATCH Commun. Math. Comput. Chem., 74 No. 2 (2015) 321-332.
[8] I. Gutman, Hyperenergetic molecular graphs, J. Serb. Chem. Soc., 64 No. 3 (1999) 199-205.
[9] I. Gutman, N. M. M. Abreu, C. T. M. Vinagre, A. S. Bonifácioa and S. Radenković, Relation between energy and Laplacian energy, MATCH Commun. Math. Comput. Chem., 59 No. 2 (2008) 343-354.
[10] F. Harary and A. J. Schwenk, Which graphs have integral spectra?, In Graphs and Combin.: Proceedings of the Capital Conference on Graph Theory and Combinatorics at the George Washington University, Springer Berlin Heidelberg, 406 (1974) 45-51.
[11] M. Herzog, M. Longobardi and M. Maj, On a commuting graph on conjugacy classes of groups, Comm. Algebra, 37 No. 10 (2009) 3369-3387.
[12] A. Mohammadian, A. Erfanian, D. G. M. Farrokhi and B. Wilkens, Triangle-free commuting conjugacy class graphs, J. Group Theory, 19 No. 6 (2016) 1049-1061.
[13] M. A. Salahshour and A. R. Ashrafi, Commuting conjugacy class graph of finite CA-groups, Khayyam J. Math., 6 No. 1 (2020) 108-118.
[14] F. Tura, L-borderenergetic graphs, MATCH Commun. Math. Comput. Chem., 77 No. 1 (2017) 37-44.
[15] H. B. Walikar, H. S. Ramane and P. R. Hampiholi, On the energy of a graph, Graph Connections, Allied Publishers, New Delhi, 120-123, 1999.
Algebraic Structures and Their Applications
Volume 12, Issue 1
February 2025
Pages 33-49

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