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Resistance distance in wheels and fans

Author

Listed:
  • R. B. Bapat

    (Indian Statistical Institute)

  • Somit Gupta

    (National Institute of Technology Karnataka)

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.

Suggested Citation

  • R. B. Bapat & Somit Gupta, 2010. "Resistance distance in wheels and fans," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(1), pages 1-13, February.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:1:d:10.1007_s13226-010-0004-2
    DOI: 10.1007/s13226-010-0004-2
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    Cited by:

    1. Sajjad, Wasim & Sardar, Muhammad Shoaib & Pan, Xiang-Feng, 2024. "Computation of resistance distance and Kirchhoff index of chain of triangular bipyramid hexahedron," Applied Mathematics and Computation, Elsevier, vol. 461(C).
    2. Wu, Zhiqiang & Xue, Yumei & He, Huixia & Zeng, Cheng & Wang, Wenjie, 2024. "Kirchhoff index of Vicsek polygon networks and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    3. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Shou-Jun, 2024. "Computation of the resistance distance and the Kirchhoff index for the two types of claw-free cubic graphs," Applied Mathematics and Computation, Elsevier, vol. 473(C).

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