The conjugacy class graph of some finite groups and its energy
DOI:
https://doi.org/10.11113/mjfas.v13n4.743Keywords:
Energy of Graph, Conjugacy Class Graph, Adjacency Matrix And Eigenvalues.Abstract
The energy of a graph which is denoted by is defined to be the sum of the absolute values of the eigenvalues of its adjacency matrix. In this paper we present the concepts of conjugacy class graph of dihedral groups and introduce the general formula for the energy of the conjugacy class graph of dihedral groups. The energy of any dihedral group of order in different cases, depends on the parity of is proved in this paper. Also we introduce the general formula for the conjugacy class graph of generalized quaternion groups and quasidihedral groups.
References
Bapat, R. B. 2010. Graphs and Matrices. New York: Springer.
Gutman, I. 1978. The Energy of Graph. Der. Math. stat. Sekt. Forschungszent Graz. 103:1-22.
Coulson, C. A., O'Leary, B., and Mallion, R. B. 1978. Hückel theory for organic chemists. Academic Pr.
Tolue, B. and Erfanian, A. 2013. Relative non-commuting graph of a finite group. Journal of Algebra and Its Applications. 12(02): 1250157.
Pirzada, S. and Gutman, I. 2008. Energy of Graph is Never the Square Root of an Odd IntegerApplication Analysis and Mathematics, . 2: 118-121.
Das, K. C. and Mojalal, S. A. 2016. On Energy and Laplacian Energy of Graphs. Electronic Journal of Linear Algebra. 31(1): 167-186.
Erfanian, A. and Tolue, B. 2013. Relative n-th non-commuting graphs of finite groups. Bulletin of the Iranian Mathematical Society. 39(4): 663-674.
Mazorodze, J. P., Mukwembi, S., and Vetrík, T. 2014. On the Gutman index and minimum degree. Discrete Applied Mathematics. 173: 77-82.
Nikiforov, V. 2007. Graphs and matrices with maximal energy. Journal of mathematical analysis and applications. 327(1): 735-738.
A., B. E., M., H., and A., M. 1990. On a Graph Related to Conjugacy Classes of Groups. Bull London Math Soc. 22: 569-575.
Omer, S. M. S., Sarmin, N. H., and Erfanian, A. 2015. Generalized conjugacy class graph of some finite non-abelian groups. 1660: 050074.
Beineke, L. W., and Wilson, R. J. 2007. Topics in Algebraic Graph Theory, Combinatorics, Probability & Computing. United States of America: Cambridge University Press.
Balakrishnan, R. 2004. The energy of a graph. Linear Algebra and its Applications. 387: 287-295.
Gutman, I. and Zhou, B. 2006. Laplacian energy of a graph. Linear Algebra and its Applications. 414(1): 29-37.
Samaila, D., Abba, B. I., and Pur, M. P. 2013. On the Conjugacy Classes, Centers and Representation of the Groups Sn and Dn. Int. J. Pure Appl. Sci. Technol. 15(1): 87-95.