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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. June 2004, Volume 3, Number 6, 335-349 |
The Branching Number of a Molecular Graph
Qian-Nan Hu and Yi-Zeng Liang
Internet Electron. J. Mol. Des. 2004, 3, 335-349
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Abstract:
Based on the structure information of the mathematical
characteristics of the degree distribution of saturated
hydrocarbons, a method to count the branching number of a
saturated hydrocarbon is proposed and then extended to general
molecules. In order to understand the structure information of
the characteristics, some new concepts are introduced, and the
edges in a molecule are partitioned into different cases. In the
understanding, the edges that are essential to connecting the
cycles are not considered as the branches. Subsequently,
several formulas are tried to calculate the proposed branching
number. Then, the formulas are generalized to other molecules
with poly-cycles, heteroatoms and/or multiple bonds. Most of
molecules are counted in agreement with intuitive view, but
there also exits some molecules that are difficult to judge the
branching numbers. The method offers an automatic and easy
way to count the branching number of a molecular graph. The
branching number is applied to be one of the classifiers to
simplify the structure diversity, and the regression results are
improved greatly. A new method, orthogonal block variables
combining with canonical correlation analysis, is also used in
the regression, which can avoid collinearity and includes, at the
same time reducing the variable dimension significantly,
almost all the information of original variables.
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