Noam Benson-Tilsen

Noam Benson-Tilsen

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Total difference chromatic numbers of regular infinite graphs

2023-12-09

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 \(\{1, 2, \ldots, k\}\) satisfying \( f(\{u,v\}) = |f(u) - f(v)| \) for any edge \(\{u,v\}\). If \( G \) is a graph, then \( \chi_{\text{td}}(G) \) 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 \( \chi_{\text{td}}(K_n) \) and also by proving results concerning infinite regular graphs.


Citation: Benson-Tilsen, Noam, et al. "Total difference chromatic numbers of regular infinite graphs." Involve, a Journal of Mathematics, vol. 16, no. 5, 9 Dec. 2023, pp. 765–781, doi.org/10.2140/involve.2023.16.765.

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