2024/04/23 by Aida Abiad, Abiad, Aida, Alessandro Neri +3 · 5 citations
Engineering · #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2404.14839
openalex publication_date 2024/04/23 · openalex created_date 2024/04/26 · openalex updated_date 2026/07/28
We derive eigenvalue bounds for the t-distance chromatic number of a graph, which is a generalization of the classical chromatic number. We apply such bounds to hypercube graphs, providing alternative spectral proofs for results by Ngo, Du and Graham [Inf. Process. Lett., 2002], and improving their bound for several instances. We also apply the eigenvalue bounds to Lee graphs, extending results by Kim and Kim [Discrete Appl. Math., 2011]. Finally, we provide a complete characterization for the existence of perfect Lee codes of minimum distance 3. In order to prove our results, we use a mix of spectral and number theory tools. Our results, which provide the first application of spectral methods to Lee codes, illustrate that such methods succeed to capture the nature of the Lee metric.