The Hopf Algebra of graph invariants
Combinatorics
2015-11-19 v1
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.
Cite
@article{arxiv.1511.05843,
title = {The Hopf Algebra of graph invariants},
author = {Nicolas Borie},
journal= {arXiv preprint arXiv:1511.05843},
year = {2015}
}
Comments
12 pages, submitted to FPSAC2016