637 research outputs found
The Wiener polarity index of benzenoid systems and nanotubes
In this paper, we consider a molecular descriptor called the Wiener polarity
index, which is defined as the number of unordered pairs of vertices at
distance three in a graph. Molecular descriptors play a fundamental role in
chemistry, materials engineering, and in drug design since they can be
correlated with a large number of physico-chemical properties of molecules. As
the main result, we develop a method for computing the Wiener polarity index
for two basic and most commonly studied families of molecular graphs, benzenoid
systems and carbon nanotubes. The obtained method is then used to find a closed
formula for the Wiener polarity index of any benzenoid system. Moreover, we
also compute this index for zig-zag and armchair nanotubes
Discrete orthogonal polynomials and difference equations of several variables
The goal of this work is to characterize all second order difference
operators of several variables that have discrete orthogonal polynomials as
eigenfunctions. Under some mild assumptions, we give a complete solution of the
problem.Comment: minor typos correcte
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