Recursive calculation of effective resistances in distance-regular networks based on Bose-Mesner algebra and Christoffel-Darboux identity
| dc.creator | Jafarizadeh, M. A. | |
| dc.creator | Sufiani, R. | |
| dc.creator | Jafarizadeh, S. | |
| dc.date | 2007-05-17 | |
| dc.date.accessioned | 2026-07-07T08:02:00Z | |
| dc.date.available | 2026-07-07T08:02:00Z | |
| dc.description | Recently in \cite{jss1}, the authors have given a method for calculation of the effective resistance (resistance distance) on distance-regular networks, where the calculation was based on stratification introduced in \cite{js} and Stieltjes transform of the spectral distribution (Stieltjes function) associated with the network. Also, in Ref. \cite{jss1} it has been shown that the resistance distances between a node $α$ and all nodes $β$ belonging to the same stratum with respect to the $α$ ($R_{αβ^{(i)}}$, $β$ belonging to the $i$-th stratum with respect to the $α$) are the same. In this work, an algorithm for recursive calculation of the resistance distances in an arbitrary distance-regular resistor network is provided, where the derivation of the algorithm is based on the Bose-Mesner algebra, stratification of the network, spectral techniques and Christoffel-Darboux identity. It is shown that the effective resistance on a distance-regular network is an strictly increasing function of the shortest path distance defined on the network. In the other words, the two-point resistance $R_{αβ^{(m+1)}}$ is strictly larger than $R_{αβ^{(m)}}$. The link between the resistance distance and random walks on distance-regular networks is discussed, where the average commute time (CT) and its square root (called Euclidean commute time (ECT)) as a distance are related to the effective resistance. Finally, for some important examples of 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} | |
| dc.description | 37 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0705.2480 | |
| dc.identifier | http://arxiv.org/abs/0705.2480 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129098 | |
| dc.subject | Combinatorics | |
| dc.title | Recursive calculation of effective resistances in distance-regular networks based on Bose-Mesner algebra and Christoffel-Darboux identity | |
| dc.type | text |