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Recently in \cite{jss1}, the authors have given a method for calculation ofthe effective resistance (resistance distance) on distance-regular networks,where the calculation was based on stratification introduced in \cite{js} andStieltjes transform of the spectral distribution (Stieltjes function)associated with the network. Also, in Ref. \cite{jss1} it has been shown thatthe resistance distances 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 $i$-th stratum with respectto the $\alpha$) are the same. In this work, an algorithm for recursivecalculation of the resistance distances in an arbitrary distance-regularresistor network is provided, where the derivation of the algorithm is based onthe Bose-Mesner algebra, stratification of the network, spectral techniques andChristoffel-Darboux identity. It is shown that the effective resistance on adistance-regular network is an strictly increasing function of the shortestpath distance defined on the network. In the other words, the two-pointresistance $R_{\alpha\beta^{(m+1)}}$ is strictly larger than$R_{\alpha\beta^{(m)}}$. The link between the resistance distance and randomwalks on distance-regular networks is discussed, where the average commute time(CT) and its square root (called Euclidean commute time (ECT)) as a distanceare related to the effective resistance. Finally, for some important examplesof finite distance- regular networks, the resistance distances are calculated.  {\bf Keywords: resistance distance, association scheme, stratification,distance-regular networks, Christoffel-Darboux identity}  {\bf PACs Index: 01.55.+b, 02.10.Yn}

Recursive calculation of effective resistances in distance-regular networks based on Bose–Mesner algebra and Christoffel–Darboux identity