A graph polynomial is weakly distinguishing if for almost all finite graphs there is a finite graph that is not isomorphic to with . It is weakly distinguishing on a graph property if for almost all finite graphs there is that is not isomorphic to with . We give sufficient conditions on a graph property for the characteristic, clique, independence, matching, and domination and polynomials, as well as the Tutte polynomial and its specializations, to be weakly distinguishing on . 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 .
"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