Variable neighborhood search for extremal graphs.: 10.: Comparison of irregularity indices for chemical trees
Variable neighborhood search for extremal graphs.: 10.: Comparison of irregularity indices for chemical trees
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DOI：
10.1021/ci0342775
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发表时间：
2005-03-01
影响因子：
5.6
通讯作者：
Mélot, H
中科院分区：
文献类型：
--
作者：
Gutman, I;Hansen, P;Mélot, H
化学图和其它图一样，如果其顶点的度相同，则化学图是正则的。否则，他们是不规则的，它是有趣的，以衡量其不规则性的描述性目的和QSAR/QSPR研究。三个指数已提出在文献中为此目的：那些Collatz Sinogowitz，艾伯森，和贝尔的方差度。我们研究他们的化学树的情况下的性质。结构示意图是用AutoGraphiX系统生成的，其中大部分后来用数学方法证明。得到了极值的解析表达式，并对最后两个指标给出了极值图的特征。
Chemical graphs, as other ones, are regular if all their vertices have the same degree. Otherwise, they are irregular, and it is of interest to measure their irregularity both for descriptive purposes and for QSAR/QSPR studies. Three indices have been proposed in the literature for that purpose: those of Collatz-Sinogowitz, of Albertson, and of Bell's variance of degrees. We study their properties for the case of chemical trees. Structural conjectures are generated with the system AutoGraphiX, and most of them proved later by mathematical means. Analytical expressions for extremal values are obtained, and extremal graphs are characterized for the two last indices.