Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems
Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems
复制标题
DOI：
10.1016/j.amc.2015.10.063
复制
发表时间：
2016-01
期刊：
影响因子：
--
通讯作者：
Ailian Chen;Xianzhu Xiong;Fenggen Lin
中科院分区：
文献类型：
--
作者：
Ailian Chen;Xianzhu Xiong;Fenggen Lin
摘要 图 G 的维纳指数 W (G) 和边维纳指数 We (G) 分别定义为图 G 中所有顶点对之间的距离之和以及 G 中所有边对之间的距离之和。维纳指数由于其与有机分子的大量物理化学性质的相关性及其有趣且不平凡的数学性质，在理论和化学文献中得到了广泛的研究。 G 的边维纳指数只不过是 G 的线图的维纳指数。线图的概念在化学研究中有着多种应用。在本文中，我们证明，如果 G 是具有 h 个六边形的降稠六方晶系，并且具有 t 个长度为 l (S i)= l i (1≤ i≤ t) 的线性段 S 1, S 2,…, St t，则 We e (G)= 25 16 W (G)+ 1 16 (120 h 2+ 94 h+ 29)− 1 4Σ i= 1 t (li− 1) 2. 我们的主要结果减少了问题 将边维纳指数上的那些与缩聚六方晶系中维纳指数上的那些相比，这使得前者更容易。
Abstract The Wiener index W (G) and the edge-Wiener index W e (G) of a graph G are defined as the sum of all distances between pairs of vertices in a graph G and the sum of all distances between pairs of edges in G, respectively. The Wiener index, due to its correlation with a large number of physico-chemical properties of organic molecules and its interesting and non-trivial mathematical properties, has been extensively studied in both theoretical and chemical literature. The edge-Wiener index of G is nothing but the Wiener index of the line graph of G. The concept of line graph has been found various applications in chemical research. In this paper, we show that if G is a catacondensed hexagonal system with h hexagons and has t linear segments S 1, S 2,…, S t of lengths l (S i)= l i (1≤ i≤ t), then W e (G)= 25 16 W (G)+ 1 16 (120 h 2+ 94 h+ 29)− 1 4∑ i= 1 t (l i− 1) 2. Our main result reduces the problems on the edge-Wiener index to those on the Wiener index in the catacondensed hexagonal systems, which makes the former ones easier.