细分网络上归一化拉普拉斯算子的群逆矩阵

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-01-01 DOI:10.2298/aadm180420023c

Ángeles Carmona Mejías, Margarida Mitjana Riera, Enrique P.J. Monsó Burgués

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引用次数: 0

摘要

本文考虑给定网络的一个细分，并证明了细分网络的归一化拉普拉斯算子的群逆矩阵与初始给定网络的归一化拉普拉斯算子的群逆矩阵之间的关系。我们的方法建立了两个结构上相关泊松问题的解之间的关系，并利用了群逆矩阵的性质。由此得到了有效电阻的计算公式和细分网络的Kirchhoff指数，用其在基网中的对应表示。最后，我们研究了两个分别以星形和轮形为基础网络的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Group inverse matrix of the normalized Laplacian on subdivision networks

In this paper we consider a subdivision of a given network and we show how the group inverse matrix of the normalized laplacian of the subdivision network is related to the group inverse matrix of the normalized laplacian of the initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both structures and takes advantage on the properties of the group inverse matrix. As a consequence we get formulae for effective resistances and the Kirchhoff Index of the subdivision network expressed in terms of its corresponding in the base network. Finally, we study two examples where the base network are the star and the wheel, respectively.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.