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Complete \(r\)-partite Graphs Determined by their Domination Polynomial

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Abstract

The domination polynomial of a graph is the polynomial whose coefficients count the number of dominating sets of each cardinality. A recent question asks which graphs are uniquely determined (up to isomorphism) by their domination polynomial. In this paper, we completely describe the complete \(r\)-partite graphs which are; in the bipartite case, this settles in the affirmative a conjecture of Aalipour et al. (Ars Comb, 2014).

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Acknowledgments

We would like to thank Ghodratollah Aalipour for providing us with preprints of [2] and [1].

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Authors and Affiliations

  1. Southwestern University, 1001 E. University Ave, Georgetown, TX, 78626, USA

    Barbara M. Anthony

  2. California State University San Marcos, San Marcos, CA, 92096, USA

    Michael E. Picollelli

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  1. Barbara M. Anthony
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  2. Michael E. Picollelli
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Correspondence to Michael E. Picollelli.

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Anthony, B.M., Picollelli, M.E. Complete \(r\)-partite Graphs Determined by their Domination Polynomial. Graphs and Combinatorics 31, 1993–2002 (2015). https://doi.org/10.1007/s00373-014-1521-2

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  • DOI: https://doi.org/10.1007/s00373-014-1521-2

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