Aromaticity of carbon nanotubes.

Carbon nanotubes are composed of cylindrical graphite sheets. Both nanotubes and graphite sheets are benzenoid derivatives composed of sp2 carbon atoms arranged in a hexagonal pattern. Therefore both systems are aromatic.

Alkane isomers: presence in petroleum ether and complexity.

The presence and absence of alkane isomers in petroleum and petroleum derivatives depend on the complexity of these structures. It was assumed that the more complex the structure is the less probable it is that that the molecule can be detected in any petroleum derivative. Complexity is a vague concept, which has not been defined in quantitative terms yet, and therefore there is no experimental method, which could be used to determine 'complexity'.

Resonance energy in graphite.

According to Zhu et al. the resonance energy/electron (REPE) in infinite graphite sheets is equal to 0.17 eV.

Enumeration of conjugated circuits in nanotubes.

The resonance energy of (1,1)n "armchair" carbon nanotubes and (n,n)1 nanoribbons was determined by enumerating the conjugated circuits (CC) and the Kekulé structures. The lower indices denote the number of hexagon layers. It was found that the resonance energy per carbon atom is equal to 0.

Atomic walk counts of negative order.

Atomic walk counts (awc's) of order k (k > or = 1) are the number of all possible walks of length k which start at a specified vertex (atom) i and end at any vertex j separated by m (0 < or = m < or = k) edges from vertex i. The sum of atomic walk counts of order k is the molecular walk count (mwc) of order k. The concept of atomic and molecular walk counts was extended to zero and negative orders by using a backward algorithm based on the usual procedure used to obtain the values of mwc's.