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arXiv · 2206.08323

Signatures of graphs for bicommutative Hopf algebras

Diego Caudillo·Joscha Diehl·Kurusch Ebrahimi-Fard·Emanuele Verri
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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.

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Diego Caudillo, Joscha Diehl, Kurusch Ebrahimi-Fard, Emanuele Verri. 2023-02-04. Signatures of graphs for bicommutative Hopf algebras. https://doi.org/10.1007/s00373-025-02907-8

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