TY - JOUR
T1 - Generalized graph splines and the Universal Difference Property
AU - Altınok, Selma
AU - Anders, Katie
AU - Arreola, Daniel
AU - Asencio, Luisa
AU - Ireland, Chloe
AU - Sarıoğlan, Samet
AU - Smith, Luke
N1 - Publisher Copyright:
© 2024 Elsevier B.V.
PY - 2024/6
Y1 - 2024/6
N2 - 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.
AB - 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.
KW - Generalized graph splines
KW - Universal Difference Property
UR - https://www.scopus.com/pages/publications/85186991999
UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=performanshacettepe&SrcAuth=WosAPI&KeyUT=WOS:001210177000001&DestLinkType=FullRecord&DestApp=WOS_CPL
U2 - 10.1016/j.disc.2024.113949
DO - 10.1016/j.disc.2024.113949
M3 - Article
AN - SCOPUS:85186991999
SN - 0012-365X
VL - 347
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 6
M1 - 113949
ER -