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Volume 22, Issue 2
  • ISSN: 1570-1794
  • E-ISSN: 1875-6271

Abstract

Introduction

The objective of this study is to compute the Kirchhoff index and resistance distance for two classes of windmill graphs, namely the French windmill graph and the Dutch windmill graph.

Methods

In this study, considered a simple connected graph with vertex set and edge set . is supposed to represent a network derived from by substituting a 1-ohm resistor for each edge of . In that case, the resistance between ϵ is considered analogous to the resistance between two equivalent nodes in network . We employed techniques from electrical network theory to compute the resistance distance and Kirchhoff index.

Results

The Kirchhoff index of is the sum of the resistance distances between all pairs of vertices in . Our computations revealed specific patterns and relationships in the resistance distances and Kirchhoff indices across different classes of windmill graphs.

Conclusion

In addition, the Kirchhoff index and resistance distance are computed in this study for specific generalizations of these graphs. The derived equations can inspire further investigation into the resistance distance and Kirchhoff index in real-world windmill networks. Additionally, they offer a chemical framework for future research, aiding in the determination of molecular structures and characteristics.

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2025-04-20

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/content/journals/cos/10.2174/0115701794299562240606054510
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Resistance Distance and Kirchhoff Index in Windmill Graphs
Curr. Org. Synth. 22, 159 (2025); https://doi.org/10.2174/0115701794299562240606054510
/content/journals/cos/10.2174/0115701794299562240606054510
/content/journals/cos/10.2174/0115701794299562240606054510
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  • Article Type:     Research Article
Keyword(s): Distance; kirchhoff index; network; resistance distance; star-mesh transformation; windmill graphs

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