A Numerical Method for Computing the Wiener Index of One-Heptagonal Carbon Nanocone
A Numerical Method for Computing the Wiener Index of One-Heptagonal Carbon Nanocone
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DOI：
10.1166/jctn.2009.1168
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发表时间：
2009-05
影响因子：
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通讯作者：
Mohammad Amin Alipour;A. Ashrafi
中科院分区：
文献类型：
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作者：
Mohammad Amin Alipour;A. Ashrafi
在过去的几年里，涉及碳的纳米结构一直是一项紧张的研究活动的焦点，这在很大程度上是由于对具有特定应用的新材料的追求。GE和Sattler在1994.1首次发现了一个五角形的碳纳米锥体。这些五角形的碳纳米锥体是从石墨烯薄片上移除60个楔子并连接边缘而形成的，在顶端有一个五角形的缺陷。六角形晶格中的七边形导致负曲率的出现，图1。理论上研究了平面石墨烯晶格中的单七重，但遗憾的是，在实验中还没有观察到这种情况。2我们首先描述一些将一直保留的符号。设G是一个无向多边无环的简单分子图，其顶点和边集分别用V G和E G表示。图G的拓扑指数是与G有关的一个数值。最古老的拓扑指数是由Harold Wiener3提出的Wiener指数。3 Diudea和他的合著者对纳米管的几何结构和它们的拓扑指数做了最重要的工作。4-9作者之一(ARA)继续这个程序计算了其他一些纳米结构的Wiener指数。10-15在一些研究论文中他们计算了一些纳米管和纳米环的Wiener指数。我们鼓励读者参考16-19和其中的参考文献，以获得背景材料和基本的计算技术。在这篇文章中，我们继续这个程序来计算维纳指数
In the past years, nanostructures involving carbon have been the focus of an intense research activity which is driven to a large extent by the quest for new materials with specific applications. One pentagonal carbon nanocones originally discovered by Ge and Sattler in 1994.1 These are constructed from a graphene sheet by removing a 60 wedge and joining the edges produces a cone with a single pentagonal defect at the apex. The inclusion of the heptagons in the hexagonal lattice leads to the appearance of negative curvature, Figure 1. The single sevenfold in the plain graphene lattice was theoretically studied but this situation, unfortunately, has not been observed in the experiment yet.2 We first describe some notations which will be kept throughout. Let G be a simple molecular graph without directed and multiple edges and without loops, the vertex and edge-sets of which are represented by V G and E G , respectively. A topological index of a graph G is a numeric quantity related to G. The oldest topological index is the Wiener index which introduced by Harold Wiener.3 The most important works on the geometric structures of nanotubes, nanotori and their topological indices were done by Diudea and his co-authors.4–9 One of the present authors (ARA) continued this program to calculate the Wiener index of some other nanostructures.10–15 In some research papers they computed the Wiener index of some nanotubes and nanotori. We encourage the reader to consult16–19 and references therein for background material as well as basic computational techniques. In this paper, we continue this program to compute the Wiener index of