Resistance Distance and Kirchhoff Index in Windmill Graphs

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: . We employed techniques from electrical network theory to compute the resistance distance and Kirchhoff index. RESULTS: . 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.