Polynomial invariants of cyclically ordered graphs
Combinatorics
2025-11-18 v1
Abstract
Cyclically ordered graphs, or cogs, sit between abstract graphs and cellularly embedded graphs. They arise naturally in topological graph theory, knot theory, and mathematical biology. We develop a formal theory of cogs and establish a number of invariants of cogs. In particular we detail several ways to present cogs and detail how these descriptions can be used to construct cog invariants by adapting the matching, transition and Yamada polynomials.
Cite
@article{arxiv.2511.13302,
title = {Polynomial invariants of cyclically ordered graphs},
author = {Paul Bratch and M. N. Ellingham and Joanna A. Ellis-Monaghan and Iain Moffatt and Wout Moltmaker},
journal= {arXiv preprint arXiv:2511.13302},
year = {2025}
}
Comments
32 pages, 10 figures