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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