Generalized graph splines and the Universal Difference Property
Combinatorics
2023-09-07 v2
Abstract
We study the generalized graph splines introduced by Gilbert, Tymoczko, and Viel and focus on an attribute known as the Universal Difference Property (UDP). We prove that paths, trees, and cycles satisfy UDP. We explore UDP on graphs pasted at a single vertex and use Pr\"ufer domains to illustrate that not every edge labeled graph satisfies UDP. We show that UDP must hold for any edge labeled graph over a ring if and only if is a Pr\"ufer domain. Lastly, we prove that UDP is preserved by isomorphisms of edge labeled graphs.
Keywords
Cite
@article{arxiv.2206.06981,
title = {Generalized graph splines and the Universal Difference Property},
author = {Selma Altınok and Katie Anders and Daniel Arreola and Luisa Asencio and Chloe Ireland and Samet Sarıoğlan and Luke Smith},
journal= {arXiv preprint arXiv:2206.06981},
year = {2023}
}