Bapat, R. B. ; Gupta, Somit (2010) Resistance distance in wheels and fans Indian Journal of Pure and Applied Mathematics, 41 (1). pp. 1-13. ISSN 0019-5588
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Official URL: http://www.springerlink.com/content/bx1j75x43x8u12...
Related URL: http://dx.doi.org/10.1007/s13226-010-0004-2
Abstract
The wheel graph is the join of a single vertex and a cycle, while the fan graph is the join of a single vertex and a path. The resistance distance between any two vertices of a wheel and a fan is obtained. The resistances are related to Fibonacci numbers and generalized Fibonacci numbers. The derivation is based on evaluating determinants of submatrices of the Laplacian matrix. A combinatorial argument is also illustrated. A connection with the problem of squaring a rectangle is described.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Indian National Science Academy. |
| Keywords: | Wheel Graph; Fan Graph; Resistance Distance; Generalized Fibonacci Numbers; Squaring A Rectangle |
| ID Code: | 81589 |
| Deposited On: | 07 Feb 2012 05:11 |
| Last Modified: | 07 Feb 2012 05:11 |
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