Critical groups of covering, voltage, and signed graphs
Combinatorics
2020-06-09 v3
Abstract
Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above kernel can be identified with a naturally defined voltage graph critical group. For double covers, the voltage graph is a signed graph, and the theory takes a particularly pleasant form, leading also to a theory of double covers of signed graphs.
Cite
@article{arxiv.1301.2977,
title = {Critical groups of covering, voltage, and signed graphs},
author = {Victor Reiner and Dennis Tseng},
journal= {arXiv preprint arXiv:1301.2977},
year = {2020}
}
Comments
Version 3 fixes a typo, and adds some details in the proof of Theorem 1.1