Kirchhoff indexes of a network
A definition of the \textsl{effective resistance between any pair of vertices with respect to a value \(\lambda \geq 0\) and a weight \(w\)} on the vertex set of a network is developed, underlying the treatment of a generalization of the Kirchhoff index of a finite network. Connections are explored between the effective resistance and eigenvalues of the associated Schrödinger operator. Explicit expressions for effective resistances are derived, which enable the calculation of effective resistances and the generalized Kirchoff index for two sparse families of networks, ``wagon-wheels'' and ``circular ladders''.
scientific article; zbMATH DE number 5689444