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Optimal Domination Polynomials

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Abstract

Let G be a graph on n vertices and m edges and D(G, x) the domination polynomial of G. In this paper we completely characterize the values of n and m for which optimal graphs exist for domination polynomials. We also show that there does not always exist least optimal graphs for the domination polynomial. Applications to network reliability are highlighted.

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Acknowledgements

J.I. Brown acknowledges support from NSERC (Grant application RGPIN 170450- 2013). D. Cox acknowledges research support from NSERC (Grant application RGPIN 2017-04401).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 4R2, Canada

    Iain Beaton & Jason I. Brown

  2. Department of Mathematics, Mount Saint Vincent University, Halifax, NS, B3M 2J6, Canada

    Danielle Cox

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  1. Iain Beaton
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  2. Jason I. Brown
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  3. Danielle Cox
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Correspondence to Danielle Cox.

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Beaton, I., Brown, J.I. & Cox, D. Optimal Domination Polynomials. Graphs and Combinatorics 36, 1477–1487 (2020). https://doi.org/10.1007/s00373-020-02202-8

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  • DOI: https://doi.org/10.1007/s00373-020-02202-8

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