A formula for the Kirchhoff index

作者：Bendito Enrique; Carmona Angeles^*; Encinas Andres M; Gesto Jose M

来源：International Journal of Quantum Chemistry, 2008, 108(6): 1200-1206.

DOI：10.1002/qua.21588

• kirchhoff index
• effective resistance
• distance-regular graphs
• equilibrium measures
• Wiener capacity

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.

• 出版日期2008-5