Bapat, R.B.Gupta, S.2026-02-052010Indian Journal of Pure and Applied Mathematics, 2010, 41, 1, pp. 1-13195588https://doi.org/10.1007/s13226-010-0004-2https://idr.nitk.ac.in/handle/123456789/27500The 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.Fan graphGeneralized Fibonacci numbersResistance distanceSquaring a rectangleWheel graph