Bounds of HOMO-LUMO Gap for Certain Nanotubes and Nanotori

Uzma Ahmad, Saira Hameed


The eigenspectrum \(\mu_1 \ge \mu_2\le \cdots \ge \mu_m\) with the middle eigenvalues \(\mu_h\) and \(\mu_l\), 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 \(\Delta_{G'}\) is defined as \(\Delta_{G'}= \mu_h-\mu_l\) 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.


Molecular graph; Eigenspectrum; HOMO-LUMO gap; Bipartite graphs; Hermitian matrix

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