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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. July 2005, Volume 4, Number 7, 491-500 |
On the Degeneracy of Topological Index J
Damir Vukicevic and Alexandru T. Balaban
Internet Electron. J. Mol. Des. 2005, 4, 491-500
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Abstract:
The topological index J is one of the widely used indices
for QSAR and QSPR studies, and has the advantage of
discriminating nonisomorphic graphs that represent
molecules of restricted size. It is of interest to see if this
property can be generalized for any connected graph. A
proof is provided for the theorem stating that for almost all
connected graphs G there is a nonisomorphic graph G' such
that G and G' have the same topological index J. Since
index J is among the least degenerate topological indices,
our results imply that a fortiori other topological indices
are even more degenerate. Hence, none of them can be used
in discrimination of general graphs.
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