Bounds of HOMO-LUMO Gap for Certain Nanotubes and Nanotori (Journal of Informatics and Mathematical Sciences, 2018)
The eigenspectrum \(μ_1 \ge μ_2\le … \ge μ_m\) with the middle eigenvalues \(μ_h\) and \(μ_l\), where \(h = \lfloor(m + 1)=2\rfloor\) and \(l = \rceil(m + 1)=2\rceil\) of simple connected graph \(G'\) with \(m\) number of vertices contribute significantly in the Huuckel Molecular Theory. The HOMO-LUMO gap \(Δ_{G'}\) is defined as \(Δ_{G'}= μ_h-μ_l\) subject to the condition that the number of electrons are in one to one correspondence with the number of vertices. In this article, the upper bounds for the HOMO-LUMO gap corresponding to the connected graphs of nanotube \(TUC_4C_8(S)\) and \(C_4C_8\) nanotorus by using matrix theory are estimated.
Keywords: Molecular graph; Eigenspectrum; HOMO-LUMO gap; Bipartite graphs; Hermitian matrix