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. © Indian National Science Academy.
CITATION STYLE
Bapat, R. B., & Gupta, S. (2010). Resistance distance in wheels and fans. Indian Journal of Pure and Applied Mathematics, 41(1), 1–13. https://doi.org/10.1007/s13226-010-0004-2
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