On the minimal energy of unicyclic Hückel molecular graphs possessing Kekulé structures

Let GG be any unicyclic Hückel molecular graph with Kekulé structures on nn vertices where n≥8n≥8 is an even number. In [W. Wang, A. Chang, L. Zhang, D. Lu, Unicyclic Hückel molecular graphs with minimal energy, J. Math. Chem. 39 (1) (2006) 231–241], Wang et al. showed that if GG satisfies certain conditions, then the energy of GG is always greater than the energy of the radialene graph. In this paper we prove that this inequality actually holds under a much weaker condition.