Bapat, Ravindra B. ; Gutman, Ivan ; Xiaob, Wenjun (2003) A simple method for computing resistance distance Zeitschrift für Naturforschung, 58a . pp. 494-498. ISSN 0372-9516
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Official URL: http://www.znaturforsch.com/aa/v58a/s58a0494.pdf
Abstract
The resistance distance rij between two vertices vi and vj of a (connected, molecular) graph G is equal to the effective resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any edge is unity. We show how rij can be computed from the Laplacian matrix L of the graph G: Let L(i) and L(i, j) be obtained from L by deleting its i-th row and column, and by deleting its i-th and j-th rows and columns, respectively. Then rij = detL(i, j)/detL(i).
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Verlag der Zeitschrift für Naturforschung. |
| Keywords: | Resistance Distance; Laplacian Matrix; Kirchhoff Index; Molecular Graph |
| ID Code: | 77807 |
| Deposited On: | 14 Jan 2012 15:25 |
| Last Modified: | 14 Jan 2012 15:25 |
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