Optimization of eigenvalue bounds for the independence and chromatic number of graph powers
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hdl:2117/365268
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Data publicació2022-03
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Abstract
The k-thpower of a graph G=(V,E), G^k, is the graph whose vertex set is V and in which two distinct vertices are adjacent if and only if their distance in G is at most k. This article proves various eigenvalue bounds for the independence number and chromatic number of G^k which purely depend on the spectrum of G, together with a method to optimize them. Our bounds for the k-independence number also work for its quantum counterpart, which is not known to be a computable parameter in general, thus justifying the use of integer programming to optimize them. Some of the bounds previously known in the literature follow as a corollary of our main results. Infinite families of graphs where the bounds are sharp are presented as well.
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© 2022 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
CitacióAbiad, A. [et al.]. Optimization of eigenvalue bounds for the independence and chromatic number of graph powers. "Discrete mathematics", Març 2022, vol. 345, núm. 3, article 112706.
ISSN0012-365X
Versió de l'editorhttps://www.sciencedirect.com/science/article/abs/pii/S0012365X21004192?via%3Dihub
Altres identificadorshttps://arxiv.org/pdf/2010.12649.pdf
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