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Resistance distance in wheels and fans

  • R. B. BapatEmail author
  • Somit Gupta
Article

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.

Key words

Wheel graph fan graph resistance distance generalized Fibonacci numbers squaring a rectangle 

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Copyright information

© The Indian National Science Academy 2010

Authors and Affiliations

  1. 1.Indian Statistical InstituteNew DelhiIndia
  2. 2.National Institute of Technology KarnatakaSurathkalIndia

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