Let Un be the set of unicyclic molecular graphs with 3 ≤ n ≤ 8 vertices. We show that the cycle Cn has maximal Laplacian-energy-like invariant (LEL) in Un. The authors partially proving that the conjecture hold for any unicyclic molecular graph in Un, where 3 ≤ n ≤ 8 Moreover, we show that Cn has maximal energy (E) in Un for 3 ≤ n ≤ 7, but for n=8 this is not true.
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