Resistance Distance and Kirchhoff Index in Windmill Graphs

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.