Resistance distance in wheels and fans

R. B. Bapat () and Somit Gupta ()
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R. B. Bapat: Indian Statistical Institute
Somit Gupta: National Institute of Technology Karnataka

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 1, 1-13

Abstract: 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.

Keywords: Wheel graph; fan graph; resistance distance; generalized Fibonacci numbers; squaring a rectangle (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s13226-010-0004-2

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