Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900455 | Advances in Applied Mathematics | 2018 | 16 Pages |
Abstract
The effective resistance RÏ of a current generator Ï shall be defined as a ratio of the Ï-components of VÏ and IÏ. By introducing potential for voltage vectors, we present a formula for RÏ via the inverse of the weighted combinatorial Laplacian of X in codimension one. We also derive a formula for RÏ via weighted high-dimensional tree-numbers for X, providing a combinatorial interpretation for RÏ. As an application, we generalize Foster's Theorem, and discuss various high-dimensional examples.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Woong Kook, Kang-Ju Lee,