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 Jafarizadeh and Salimi (2006 J. Phys. A: Math. Gen. 39 1-29) and the Stieltjes transform of the spectral distribution (Stieltjes function) associated with the network. It is shown that the resistances between a node alpha and all nodes beta belonging to the same stratum with respect to the alpha (R-alpha beta(i), beta belonging to the ith stratum with respect to the alpha) are the same. Also, the analytical formulae for two-point resistances R-alpha beta(i), i = 1, 2, 3, are given in terms of 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 its parameters (nu, kappa, lambda, mu). Moreover, the lower and upper bounds for two- point resistances in strongly regular networks are discussed.