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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