Signatures of graphs for bicommutative Hopf algebras
Rings and Algebras
2025-03-27 v2 Combinatorics
Abstract
This article approaches the counting of subgraphs, in terms of signature-type functionals defined over combinatorial Hopf algebras of graphs. Well-known algebraic identities that arise in the context of counting subgraphs are then captured by their character property and a type of "Chen's identity". While different notions of subgraphs (and homomorphisms) correspond to different combinatorial Hopf algebras on graphs, we will show that they are all isomorphic to a polynomial Hopf algebra. In addition, the isomorphy between the Hopf algebras can be realized by maps that respect the counting operations.
Keywords
Cite
@article{arxiv.2206.08323,
title = {Signatures of graphs for bicommutative Hopf algebras},
author = {Diego Caudillo and Joscha Diehl and Kurusch Ebrahimi-Fard and Emanuele Verri},
journal= {arXiv preprint arXiv:2206.08323},
year = {2025}
}
Comments
43 pages, 1 figure