Computation of resistance distance with Kirchhoff index of body centered cubic structure

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-02-06 DOI:10.1007/s10910-023-01573-6

Wasim Sajjad, Xiang-Feng Pan, Qura tul Ain

引用次数: 0

Abstract

The two-point effective resistance of an electrical network is a classical problem in theory of electrical networks. In a graph G the resistance distance among two vertices is an effective resistance between the respective vertices in the extracted electrical network from a graph G by setting every edge of graph G with a unit resistor. The sum of resistance distance between all pairs of vertices of graph G is the Kirchhoff index. Body centered cubic unit cells are made of atoms arranged in a cube, with one atom at each corner and another atom at the center. Many chemists and mathematicians have studied the body centered cubic structure (BCC) due to its atom arrangement. Utilizing some techniques from electrical networks theory, we compute the effective resistance among every pair of vertices of body centered cubic structure (BCC). We also apply our results to derive the formula for the Kirchhoff index.

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用基尔霍夫指数计算体心立方结构的阻力距离

电气网络的两点有效电阻是电气网络理论中的一个经典问题。在图 G 中，通过给图 G 的每条边设置一个单位电阻，两个顶点之间的电阻距离即为从图 G 中提取的电气网络中各顶点之间的有效电阻。图 G 中所有顶点对之间的电阻距离之和就是基尔霍夫指数。体心立方单元是由原子排列成的立方体，每个角上有一个原子，中心有另一个原子。由于体心立方结构（BCC）的原子排列方式，许多化学家和数学家都对其进行过研究。我们利用电气网络理论的一些技术，计算了体心立方结构（BCC）每对顶点之间的有效电阻。我们还应用我们的结果推导出了基尔霍夫指数公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.