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A generalization of chromatic polynomial of a graph subdivision

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Abstract

Considering the partitions of a set into nonempty subsets, we obtain an expression for the number of all partitions of a given type. The chromatic polynomial of a graph subdivision is generalized, considering two sets of colors, and a general explicit expression is obtained for this generalization. Using these results, we determine the generalized chromatic polynomial for the particular case of complete graph subdivision.

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Authors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    D. M. Cardoso & M. E. Silva

  2. Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland

    J. Szymański

Authors
  1. D. M. Cardoso
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  2. M. E. Silva
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  3. J. Szymański
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Corresponding author

Correspondence to D. M. Cardoso.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 71, Algebraic Techniques in Graph Theory and Optimization, 2011.

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Cardoso, D.M., Silva, M.E. & Szymański, J. A generalization of chromatic polynomial of a graph subdivision. J Math Sci 182, 246–254 (2012). https://doi.org/10.1007/s10958-012-0745-z

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  • DOI: https://doi.org/10.1007/s10958-012-0745-z

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