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 α and all nodes β belonging to the same stratum with respect to the α , β belonging to the ith stratum with respect to the α) are the same. Also, the analytical formulae for two-point resistances , 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 (v, κ, λ, μ). Moreover, the lower and upper bounds for two-point resistances in strongly regular networks are discussed.