On Weakly Distinguishing Graph Polynomials
Combinatorics
2023-06-22 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1810.13300,
title = {On Weakly Distinguishing Graph Polynomials},
author = {Johann A. Makowsky and Vsevolod Rakita},
journal= {arXiv preprint arXiv:1810.13300},
year = {2023}
}