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<p>We encode graph profiles based on homomorphisms, injective homomorphisms, and embeddings as families of linear functionals. We show that these maps are compatible with the operations of their underlying combinatorial Hopf algebras. Furthermore, we give two alternative proofs that these Hopf algebras are all isomorphic to a polynomial Hopf algebra. The first is based on a classical result in the theory of Hopf algebras, while the second relies on maps that allow one to switch between the different profiles.</p>

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Graph Profiles as Characters on Bicommutative Hopf Algebras

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月21日

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  • Diego Caudillo,
  • Joscha Diehl,
  • Kurusch Ebrahimi-Fard,
  • Emanuele Verri

摘要

We encode graph profiles based on homomorphisms, injective homomorphisms, and embeddings as families of linear functionals. We show that these maps are compatible with the operations of their underlying combinatorial Hopf algebras. Furthermore, we give two alternative proofs that these Hopf algebras are all isomorphic to a polynomial Hopf algebra. The first is based on a classical result in the theory of Hopf algebras, while the second relies on maps that allow one to switch between the different profiles.