The Szeged Index and an Analogy with the Wiener Index
The Szeged Index and an Analogy with the Wiener Index
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DOI：
10.1021/ci00025a024
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发表时间：
1995-05
期刊：
影响因子：
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通讯作者：
P. Khadikar;N. Deshpande;P. P. Kale-P.;A. Dobrynin;I. Gutman;G. Dömötör
中科院分区：
文献类型：
--
作者：
P. Khadikar;N. Deshpande;P. P. Kale-P.;A. Dobrynin;I. Gutman;G. Dömötör
有机分子的最古老和最彻底的基于分子图的结构描述符之一是维纳指数或维纳数，W。1-7这个量等于各个分子图的所有顶点对之间的距离之和。如果d（n，v| G）是图G的顶点u和v的距离8（即连接u和v的最短路中的边数），V（G）是G的顶点集，则n2（e| G）是距离v比距离u近的顶点数;距离u和v等距的顶点不计算在内。上述定义具有适用于任意图的任意边的优点。（注意，在我们的定义中，并不要求图G是连通的;然而，在化学应用中，我们只遇到连通图。）有鉴于此，我们很容易想到对循环图检验（2）的右侧。另一方面，这相当于引入了一个新的拓扑指数Sz= Sz（G），10，定义为：
One of the oldest and most thoroughly examined molecular-graph-based structural descriptors of organic molecules is the Wiener index or Wiener number, W. 1-7 This quantity is equal to the sum of distances between all pairs of vertices of the respective molecular graph. If d («, v| G) is the distance8 of the vertices u and v of the graph G (ie, the number of edges in the shortest path that connects u and v), and V (G) is the vertex set of G, then n2 (e| G) is the number of vertices closer to v than to u; vertices equidistant to u and v are not counted. The above definition has the advantage of being applicable to an arbitrary edge of an arbitrary graph.(Notice that in our definition it is not required that the graph G is connected; in chemical applications, however, one encounters only connected graphs.) In view of this, it readily comes to mind to examine the right-hand side of (2) for cyclic graphs. This, on the other hand, is tantamount to the introduction of a novel topological index Sz= Sz (G), 10 defined as