@article { author = {Dutta, Parama and Bagchi, Biswadeep and Nath, Rajat}, title = {Various Energies of Commuting Graphs of Finite Nonabelian Groups}, journal = {Khayyam Journal of Mathematics}, volume = {6}, number = {1}, pages = {27-45}, year = {2020}, publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)}, issn = {2423-4788}, eissn = {2423-4788}, doi = {10.22034/kjm.2019.97094}, abstract = {The commuting graph of a finite nonabelian group  $G$ is a simple undirected graph, denoted by $\Gamma_G$, whose vertex set is the noncentral elements of $G$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = yx$. In  this paper, we compute energy,  Laplacian energy, and signless Laplacian energy of  $\Gamma_G$ for various  families of finite nonabelian groups and analyze their values graphically. Our computations show that the conjecture posed in [MATCH Commun. Math. Comput. Chem. 59, (2008) 343-354 ] holds for the commuting graph of some families of finite groups.}, keywords = {Commuting graph,spectrum,Energy,finite group}, url = {https://www.kjm-math.org/article_97094.html}, eprint = {https://www.kjm-math.org/article_97094_19bea7eef79e328fcdc7ad5118452748.pdf} }