Resistance Distance and Kirchhoff Index in Windmill Graphs

IF 1.7 4区化学 Q3 CHEMISTRY, ORGANIC

Current organic synthesis Pub Date : 2024-07-05 DOI:10.2174/0115701794299562240606054510

Muhammad Shoaib Sardar, Shou-Jun Xu

引用次数: 0

Abstract

Introduction:: The objective of this study is to compute the Kirchhoff index and re-sistance distance for two classes of windmill graphs, namely the French windmill graph and the Dutch windmill graph. Methods:: In this study, G is considered a simple connected graph with vertex set V (G) and edge set E(G). N is supposed to represent a network derived from G by substituting a 1-ohm resistor for each edge of G. In that case, the resistance between μ,ν ∈ V (G) is considered analogous to the resistance between two equivalent nodes in network N. Results:: The Kirchhoff index of G is the sum of the resistance distances between all pairs of vertices in G. Conclusion:: In addition, the Kirchhoff index and resistance distance are computed in this study for specific generalizations of these graphs.

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风车图中的电阻距离和基尔霍夫指数

导言本研究旨在计算两类风车图（即法国风车图和荷兰风车图）的基尔霍夫指数和重阻距离。方法：：在本研究中，G 被视为简单连通图，具有顶点集 V (G) 和边集 E(G)。在这种情况下，μ,ν ∈ V (G) 之间的电阻被认为类似于网络 N 中两个等效节点之间的电阻。结果：：G 的基尔霍夫指数是 G 中所有顶点对之间电阻距离的总和：此外，本研究还计算了这些图的特定广义的基尔霍夫指数和电阻距离。

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

Current organic synthesis 化学-有机化学

CiteScore

3.40

自引率

5.60%

发文量

审稿时长

6-12 weeks

期刊介绍： Current Organic Synthesis publishes in-depth reviews, original research articles and letter/short communications on all areas of synthetic organic chemistry i.e. asymmetric synthesis, organometallic chemistry, novel synthetic approaches to complex organic molecules, carbohydrates, polymers, protein chemistry, DNA chemistry, supramolecular chemistry, molecular recognition and new synthetic methods in organic chemistry. The frontier reviews provide the current state of knowledge in these fields and are written by experts who are internationally known for their eminent research contributions. The journal is essential reading to all synthetic organic chemists. Current Organic Synthesis should prove to be of great interest to synthetic chemists in academia and industry who wish to keep abreast with recent developments in key fields of organic synthesis.

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