Geodesic
On Weakly Distinguishing Graph Polynomials
Discrete mathematics & theoretical computer science, ICGT 2018, Tome 21 (2019) no. 1.

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A univariate graph polynomial P(G;X) is weakly distinguishing if for almost all finite graphs G there is a finite graph H with P(G;X)=P(H;X). We show that the clique polynomial and the independence polynomial are weakly distinguishing. Furthermore, we show that generating functions of induced subgraphs with property C are weakly distinguishing provided that C is of bounded degeneracy or tree-width. The same holds for the harmonious chromatic polynomial. 
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     author = {Makowsky, Johann A. and Rakita, Vsevolod},
     title = {On {Weakly} {Distinguishing} {Graph} {Polynomials}},
     journal = {Discrete mathematics & theoretical computer science},
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Makowsky, Johann A.; Rakita, Vsevolod. On Weakly Distinguishing Graph Polynomials. Discrete mathematics & theoretical computer science, ICGT 2018, Tome 21 (2019) no. 1. doi : 10.23638/DMTCS-21-1-4. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-1-4/

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