The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

被引：17
|
作者：
Pletersek, Petra Zigert [1 ,2 ]
机构：
[1] Univ Maribor, Fac Chem & Chem Engn, Maribor, Slovenia
[2] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia
来源：
DISCRETE APPLIED MATHEMATICS | 2019年 / 255卷
关键词：
Edge-Wiener index; Edge-hyper-Wiener index; Phenylene; Elementary cut; Quotient tree; BENZENOID SYSTEMS; SZEGED INDEX; PI INDEX; TOPOLOGICAL INDEXES; CUT METHOD; NUMBER; VERSION;
D O I：
10.1016/j.dam.2018.07.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Besides the well known Wiener index, which sums up the distances between all the pairs of vertices, and the hyper-Wiener index, which includes also the squares of distances, the edge versions of both indices attracted a lot of attention in the recent years. In this paper we consider the edge-Wiener index and the edge-hyper-Wiener index of phenylenes, which represent an important class of molecular graphs. For an arbitrary phenylene, four quotient trees based on the elementary cuts are defined in a similar way as it was previously done for benzenoid systems. The computation of the edge-Wiener index of the phenylene is then reduced to the calculation of the weighted Wiener indices of the corresponding quotient trees. Furthermore, a method for computing the edge-hyper-Wiener index of phenylenes is described. Finally, the application of these results gives closed formulas for the edge-Wiener index and the edge-hyper-Wiener index of linear phenylenes. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：326 / 333
页数：8
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