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

AbstractLet G be any unicyclic Hückel molecular graph with Kekulé structures on n vertices where n≥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 G satisfies certain conditions, then the energy of G 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