Can topological indices transmit information on properties but not on structures?
Can topological indices transmit information on properties but not on structures?
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DOI：
10.1007/s10822-005-9010-6
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发表时间：
2005-09-01
影响因子：
3.5
通讯作者：
Balaban, AT
中科院分区：
文献类型：
--
作者：
Balaban, AT
根据局部顶点不变量（LOVI）和由此产生的分子描述符（TI）的性质（整数或真实的数），提供了几种拓扑指数（TI）的调查。当LOVI和TI都是整数时，诸如Wiener指数的第一代TI具有非常高的简并性。这一事实可以成为一个资产的问题正在讨论中：当面对“逆问题”（逆向工程），这些指数导致一个组合爆炸的可能解决方案。在另一个极端，具有非常低的简并度的TI也可以提供传输关于属性而不是关于结构的信息的可能性，因为它们可能太难以在合理的时间内进行逆向工程。几个这样的指数进行了讨论：新的第二代指数G（来自平均距离为基础的连接性指数J，以包括依赖于图的大小和循环），和第三代指数，如三重TI表示（DNS）-S-2（4）或基尔霍尔指数TOTOP。G与（DNS）-S ~（-2）（4）几乎呈线性相关，而与TOTOP有不同的相关关系。
A survey of several topological indices (TIs) is provided according to the nature (integers or real numbers) of the local vertex invariants (LOVIs) and of the resulting molecular descriptor (TI). The 1st generation TIs such as the Wiener index when both the LOVIs and the TI are integers have a very high degeneracy. This fact can become an asset for the problem under discussion: when confronted with the "inverse problem" (reverse engineering) such indices lead to a combinatorial explosion of possible solutions. On the other extreme, TIs with very low degeneracy may also offer the possibility to transmit information on properties but not on structures, because they may be too difficult to lend themselves to reverse engineering in a reasonable amount of time. Several such indices are discussed: the novel second-generation index G (derived from the average distance-based connectivity index J in order to include a dependence on graph size and cyclicity), and third-generation indices such as the triplet TI denoted by (DNS)-S-2(4) or the Kier-Hall index TOTOP. The intercorrelation of these indices is discussed: G is almost linearly-correlated with (DNS)-S-2(4), and shows a different type of correlation with TOTOP.