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Matchings in hexagonal cacti

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  • E. J. Farrell

Abstract

Explicit recurrences are derived for the matching polynomials of the basic types of hexagonal cacti, the linear cactus and the star cactus and also for an associated graph, called the hexagonal crown. Tables of the polynomials are given for each type of graph. Explicit formulae are then obtained for the number of defect- d matchings in the graphs, for various values of d . In particular, formulae are derived for the number of perfect matchings in all three types of graphs. Finally, results are given for the total number of matchings in the graphs.

Suggested Citation

  • E. J. Farrell, 1987. "Matchings in hexagonal cacti," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 10, pages 1-18, January.
    • Handle: RePEc:hin:jijmms:234184
    DOI: 10.1155/S0161171287000395
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    Cited by:

    1. Chang, Caibing & Ren, Haizhen & Deng, Zijian & Deng, Bo, 2021. "The ρ‐-moments of vertex‐weighted graphs," Applied Mathematics and Computation, Elsevier, vol. 400(C).

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