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Quantum chromatic numbers of products of quantum graphs

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arxiv 2408.11911 v1 pith:7XFNCY74 submitted 2024-08-21 math.OA

Rolando de Santiago , A. Meenakshi McNamara This is my paper · ORCID
classification math.OA
keywords quantumchromaticgraphsnumberproductsboundslexicographicadequately
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abstract

We define the Cartesian, Categorical, and Lexicographic, and Strong products of quantum graphs. We provide bounds on the quantum chromatic number of these products in terms of the quantum chromatic number of the factors. To adequately describe bounds on the lexicographic product of quantum graphs, we provide a notion of a quantum $b$-fold chromatic number for quantum graphs.

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  1. Quantum chromatic numbers of some graphs in Hamming schemes

    math.CO 2024-12 conditional novelty 6.0 of 10

    The Hamming graph H(4t-1, 2t) has quantum chromatic number exactly 4t, with exact product values for related families.

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