Abstract
For any simple connected graph
of order
, having eigen spectrum
≥
≥ ⋯ ≥
with middle eigenvalues
and
, where H = ⌊(
+ 1)/2⌋ and L = ⌈(
+ 1)/2⌉, the HOMO–LUMO gap is defined as as Δ
=
=
. In this article, a simple upper bound for the HOMO–LUMO gap corresponding to a special class of connected bipartite graphs is estimated. As an application, the upper bounds for the HOMO–LUMO gap of certain classes of nanotubes and nanotori are estimated.