Graph invariants from ideas in physics and number theory
Combinatorics
2015-06-18 v3
Abstract
We study free scalar field theory on a graph, which gives rise to a modified version of discrete Green's function on a graph studied in \cite{CY}. We show that this gives rise to a graph invariant, which is closely related to the 2-dim Weisfeiler-Lehman algorithm for graph isomorphism testing. We complement this invariant by another type of graph invariants, coming from viewing graphs as quadratic forms over the integers. We explain that the combination of these two ideas give rise to an interesting approach to the graph isomorphism problem.
Cite
@article{arxiv.1409.5853,
title = {Graph invariants from ideas in physics and number theory},
author = {An Huang and Shing-Tung Yau and Mei-Heng Yueh},
journal= {arXiv preprint arXiv:1409.5853},
year = {2015}
}
Comments
26 pages, new results added