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2020 Weakly distinguishing graph polynomials on addable properties
Johann A. Makowsky, Vsevolod Rakita
Mosc. J. Comb. Number Theory 9(3): 333-349 (2020). DOI: 10.2140/moscow.2020.9.333

Abstract

A graph polynomial P is weakly distinguishing if for almost all finite graphs G there is a finite graph H that is not isomorphic to G with P(G)=P(H). It is weakly distinguishing on a graph property 𝒞 if for almost all finite graphs G𝒞 there is H𝒞 that is not isomorphic to G with P(G)=P(H). We give sufficient conditions on a graph property 𝒞 for the characteristic, clique, independence, matching, and domination and ξ polynomials, as well as the Tutte polynomial and its specializations, to be weakly distinguishing on 𝒞. One such condition is to be addable and small in the sense of C. McDiarmid, A. Steger and D. Welsh (2005). Another one is to be of genus at most k.

Citation

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Johann A. Makowsky. Vsevolod Rakita. "Weakly distinguishing graph polynomials on addable properties." Mosc. J. Comb. Number Theory 9 (3) 333 - 349, 2020. https://doi.org/10.2140/moscow.2020.9.333

Information

Received: 5 December 2019; Revised: 1 March 2020; Accepted: 19 March 2020; Published: 2020
First available in Project Euclid: 22 October 2020

zbMATH: 07272352
MathSciNet: MR4164872
Digital Object Identifier: 10.2140/moscow.2020.9.333

Subjects:
Primary: 05C31
Secondary: 05C10, 05C30, 05C69, 05C80

Rights: Copyright © 2020 Mathematical Sciences Publishers

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