(untitled) (Journal of Informatics and Mathematical Sciences, 2018)
The eigenspectrum \(μ_1 μ_2… μ_m\) with the middle eigenvalues \(μ_h\) and \(μ_l\), where \(h = (m + 1)=2 floor\) and \(l = ceil(m + 1)=2 ceil\) 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.