Calculating two-point resistances in distance-regular resistor networks

An algorithm for the calculation of the resistance between two arbitrary nodes in an arbitrary distance-regular resistor network is provided, where the calculation is based on stratification introduced in [1] and Stieltjes transform of the spectral distribution (Stieltjes function) associated with the network. It is shown that the resistances between a node α and all nodes β belonging to the same stratum with respect to the α (Rαβ(i) , β belonging to the i-th stratum with respect to the α) are the same. Also, the analytical formulas for two-point resistances Rαβ(i) , i = 1, 2, 3 are given in terms of the the size of the network and corresponding intersection numbers. In particular, the two-point resistances in a strongly regular network are given in terms of the its parameters (v, κ, λ, μ). Moreover, the lower and upper bounds for two-point resistances in strongly regular networks are discussed.