Effective Resistances for Ladder-Like Chains

摘要

Here, we consider a class of generalized linear chains; that is, the ladder-like chains as a perturbation of a 2n path by adding consecutive weighted edges between opposite vertices. This class of chains in particular includes a big family of networks that goes from the cycle, unicycle chains up to ladder networks. In this article, we obtain the Green function, the effective resistance, and the Kirchhoff index of ladder-like chains in terms of the Green function, the effective resistance, and the Kirchhoff index of the path.