In the present work, we define a partial subdivision network of a given network G, by inserting a new vertex in some selected edges of G, so that each of these edges is replaced by two new edges with conductances that fulfil the Kirchhoff series law on the new network. Then, we obtain an expression for the Green kernel of the partial subdivision network in terms of the Green kernel of the base network. For that, we show the relation between Poisson problems on the partial subdivision network and...
In the present work, we define a partial subdivision network of a given network G, by inserting a new vertex in some selected edges of G, so that each of these edges is replaced by two new edges with conductances that fulfil the Kirchhoff series law on the new network. Then, we obtain an expression for the Green kernel of the partial subdivision network in terms of the Green kernel of the base network. For that, we show the relation between Poisson problems on the partial subdivision network and Poisson problems on the base network. Moreover, we also obtain the effective resistance and the Kirchhoff index of the partial subdivision network in terms of the corresponding parameters on the base network. Finally, as an example, we carry out the computations in the case of a star network in which we have subdivided the even edges.
Citation
Carmona, A., Mitjana, M., Monso, E. Green's function in partial subdivision networks. "Linear and multilinear algebra", Vol. 68, No 1, pp.94-112