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The Hopf Algebra of graph invariants

2015/11/18 by Nicolas Borie, Borie, Nicolas
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1511.05843

openalex publication_date 2015/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an algebraic study of the simple graph isomorphism problem. We define a Hopf algebra from an explicit realization of its elements as formal power series. We show that these series can be evaluated on graphs and count occurrences of subgraphs. We establish a criterion for the isomorphism test of two simple graphs by means of occurrence counting of subgraphs. This criterion is deduced from algebraic relations between elements of our algebra.

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