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Total difference chromatic numbers of regular infinite graphs

Noam Benson-Tilsen, Samuel Brock, Brandon Faunce, Monish Kumar, Noah Dokko Stein and Joshua Zelinsky

Vol. 16 (2023), No. 5, 765–781

Given a graph G, a k-total difference labeling of the graph is a total labeling f from the set of edges and vertices to the set {1,2,,k} satisfying f({u,v}) = |f(u) f(v)| for any edge {u,v}. If G is a graph, then χtd (G) is the minimum k such that there is a k-total difference labeling of G in which no two adjacent labels are identical. We extend prior work on total difference labeling by improving the upper bound on χtd (Kn) and also by proving results concerning infinite regular graphs.

graph coloring, chromatic number
Mathematical Subject Classification
Primary: 05C15
Secondary: 05C63
Received: 3 August 2021
Revised: 6 November 2022
Accepted: 13 November 2022
Published: 9 December 2023

Communicated by Kenneth S. Berenhaut
Noam Benson-Tilsen
Cornell University
Ithaca, NY
United States
Samuel Brock
Yale University
New Haven, CT
United States
Brandon Faunce
Rochester Institute of Technology
Rochester, NY
United States
Monish Kumar
Hopkins School
New Haven, CT
United States
Noah Dokko Stein
Yale University
New Haven, CT
United States
Joshua Zelinsky
Hopkins School
New Haven, CT
United States