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arXiv · 1511.05843

The Hopf Algebra of graph invariants

Nicolas Borie
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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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Nicolas Borie. 2015-11-18. The Hopf Algebra of graph invariants. https://arxiv.org/abs/1511.05843

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