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.
Dutta, P., Bagchi, B., Nath, R. (2020). Various Energies of Commuting Graphs of Finite Nonabelian Groups. Khayyam Journal of Mathematics, 6(1), 27-45. doi: 10.22034/kjm.2019.97094
MLA
Parama Dutta; Biswadeep Bagchi; Rajat Kanti Nath. "Various Energies of Commuting Graphs of Finite Nonabelian Groups". Khayyam Journal of Mathematics, 6, 1, 2020, 27-45. doi: 10.22034/kjm.2019.97094
HARVARD
Dutta, P., Bagchi, B., Nath, R. (2020). 'Various Energies of Commuting Graphs of Finite Nonabelian Groups', Khayyam Journal of Mathematics, 6(1), pp. 27-45. doi: 10.22034/kjm.2019.97094
VANCOUVER
Dutta, P., Bagchi, B., Nath, R. Various Energies of Commuting Graphs of Finite Nonabelian Groups. Khayyam Journal of Mathematics, 2020; 6(1): 27-45. doi: 10.22034/kjm.2019.97094
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