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A formula for the Kirchhoff index |
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| Authors: | Enrique Bendito Angeles Carmona Andres M. Encinas Jose M. Gesto |
| Affiliation: | Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain |
| Abstract: | We show here that the Kirchhoff index of a network is the average of the Wiener capacities of its vertices. Moreover, we obtain a closed‐form formula for the effective resistance between any pair of vertices when the considered network has some symmetries, which allows us to give the corresponding formulas for the Kirchhoff index. In addition, we find the expression for the Foster's n‐th formula. |
| Keywords: | Kirchhoff index effective resistance distance‐regular graphs equilibrium measures Wiener capacity |