Generalized graph splines and the Universal Difference Property

ALTINOK BHUPAL, SELMA; Anders, Katie; Arreola, Daniel; Asencio, Luisa; Ireland, Chloe; SARIOĞLAN, SAMET; Smith, Luke

doi:10.1016/j.disc.2024.113949

Generalized graph splines and the Universal Difference Property

ALTINOK BHUPAL S., Anders K., Arreola D., Asencio L., Ireland C., SARIOĞLAN S., ...More

Discrete Mathematics, vol.347, no.6, 2024 (SCI-Expanded, Scopus)

Publication Type: Article / Article
Volume: 347 Issue: 6
Publication Date: 2024
Doi Number: 10.1016/j.disc.2024.113949
Journal Name: Discrete Mathematics
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
Keywords: Generalized graph splines, Universal Difference Property
Hacettepe University Affiliated: Yes

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 Prüfer 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 R if and only if R is a Prüfer domain. Lastly, we prove that UDP is preserved by isomorphisms of edge labeled graphs.