Wiener极性指标和终端Wiener指标的推广
Generalizations of Wiener polarity index and terminal Wiener index
摘要：
在理论化学中，基于距离的分子结构描述符用于模拟化合物的物理，药理学，生物学和其他性质。我们引入广义Wiener极性指数$W_k (G)$作为$G$的无序顶点对${u, v}$的数量，使得$u$和$v$之间的最短距离$d (u, v)$是$k$（这实际上是Wiener多项式中的第$k$个系数）。对于$k = 3$，我们得到标准的Wiener极性指数。此外，我们推广的终端Wiener指数$TW_k (G)$之间的距离和所有对度$k$的顶点。对于$k = 1$，我们得到标准的终端Wiener指数。在本文中，我们描述了一个线性时间算法计算这些指标的树和部分立方体，并刻画极值树最大化广义Wiener极性指数和广义终端Wiener指数之间的所有给定顺序$n$的树。
英文摘要：
In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. We introduce a generalized Wiener polarity index $W_k (G)$ as the number of unordered pairs of vertices ${u, v}$ of $G$ such that the shortest distance $d (u, v)$ between $u$ and $v$ is $k$ (this is actually the $k$-th coefficient in the Wiener polynomial). For $k = 3$, we get standard Wiener polarity index. Furthermore, we generalize the terminal Wiener index $TW_k (G)$ as the sum of distances between all pairs of vertices of degree $k$. For $k = 1$, we get standard terminal Wiener index. In this paper we describe a linear time algorithm for computing these indices for trees and partial cubes, and characterize extremal trees maximizing the generalized Wiener polarity index and generalized terminal Wiener index among all trees of given order $n$.
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