Minimizing Effective Resistance of a Graph
SIAM Review
Kirchhoff index of composite graphs
Discrete Applied Mathematics
The Kirchhoff indexes of some composite networks
Discrete Applied Mathematics
| Hi-index | 0.04 |
In this work we compute the effective resistance between any pair of vertices with respect to a value@l=0and a weight@w on the vertex set of the join network in terms of the corresponding parameters for the factors. In particular, this allows us to express the Kirchhoff index with respect to a value @l=0 and a weight @w of the join network in terms of the Kirchhoff indices of the factors. Moreover, we obtain a full description of the eigenvalues and the corresponding eigenfunctions for a positive semi-definite Schrodinger operator on a join network. Finally, we compute the effective resistances and the generalized Kirchhoff index with respect to a value @l=0 and a weight @w for some families of join networks, specifically for star and cone networks.