边-细谷多项式的一种计算方法及其在苯上的应用

IF 2.9 2区化学 Q2 CHEMISTRY, MULTIDISCIPLINARY

Match-Communications in Mathematical and in Computer Chemistry Pub Date : 2023-01-01 DOI:10.46793/match.89-3.605k

M. Knor, Niko Tratnik

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引用次数: 1

摘要

图的边-细谷多项式是著名的细谷多项式的边版本。因此，edge-Hosoya多项式计算给定图中距离k≥0处(无序)边对的个数。众所周知，该多项式与边-维纳指数和边-超维纳指数密切相关。作为本文的主要结果，我们提供了一种计算图G的边-细谷多项式的方法，这是通过识别连通二部图G1和G2的两条边得到的。为了说明主要定理的应用，我们把它应用到苯基链上。特别地，我们给出了计算任何苯基链边-细谷多项式的递归关系和线性时间算法。由此导出了线性苯基链边-细谷多项式的封闭公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A Method for Computing the Edge-Hosoya Polynomial with Application to Phenylenes

The edge-Hosoya polynomial of a graph is the edge version of the famous Hosoya polynomial. Therefore, the edge-Hosoya polynomial counts the number of (unordered) pairs of edges at distance k ≥ 0 in a given graph. It is well known that this polynomial is closely related to the edge-Wiener index and the edge-hyper-Wiener index. As the main result of this paper, we greatly generalize an earlier result by providing a method for calculating the edge-Hosoya polynomial of a graph G which is obtained by identifying two edges of connected bipartite graphs G1 and G2. To show how the main theorem can be used, we apply it to phenylene chains. In particular, we present the recurrence relations and a linear time algorithm for calculating the edge-Hosoya polynomial of any phenylene chain. As a consequence, closed formula for the edge-Hosoya polynomial of linear phenylene chains is derived.

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来源期刊

Match-Communications in Mathematical and in Computer Chemistry 化学-化学综合

CiteScore

4.40

自引率

26.90%

发文量

审稿时长

2 months

期刊介绍： MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.