Kirchhoff index of some networks based on the cluster of graph

The Kirchhoff index represents the sum of resistance distances between all pairs of nodes in a network. It reflects the integrity and connectivity of the network. In this paper, we propose three classes of network models, all generated based on the cluster of graphs. We derive exact expressions for their Kirchhoff indices through an iterative methodology. Leveraging the derived formulas, we compared the Kirchhoff indices of the network families corresponding to three classes of networks generated under the same base graph. This enhances our evaluation of network characteristics, potentially serving as a critical tool in the practical design of networks.