Various Energies of Commuting Graphs of Finite Nonabelian Groups

Document Type : Original Article


Department of Mathematical Sciences, Tezpur University, Napaam 784028, Sonitpur, Assam, India.


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.