Quantum Chromatic Number of Subgraphs of Orthogonality Graphs and the Distance-2 Hamming Graph
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915646767366144 |
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| author | Luo, Tao Ning, Yu Zhang, Xiande |
| author_facet | Luo, Tao Ning, Yu Zhang, Xiande |
| contents | The determination of the quantum chromatic number of graphs has attracted considerable attention recently. However, there are few families of graphs whose quantum chromatic numbers are determined. A notable exception is the family of orthogonality graphs, whose quantum chromatic numbers are fully determined. In this paper, we extend these results by determining the exact quantum chromatic number of several subgraphs of the orthogonality graphs. Using the technique of combinatorial designs, we also determine the quantum chromatic number of the distance-2 Hamming graph, whose edges consist of binary vectors of Hamming distance 2, for infinitely many length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Chromatic Number of Subgraphs of Orthogonality Graphs and the Distance-2 Hamming Graph Luo, Tao Ning, Yu Zhang, Xiande Combinatorics Quantum Physics 05C15, 05B30 The determination of the quantum chromatic number of graphs has attracted considerable attention recently. However, there are few families of graphs whose quantum chromatic numbers are determined. A notable exception is the family of orthogonality graphs, whose quantum chromatic numbers are fully determined. In this paper, we extend these results by determining the exact quantum chromatic number of several subgraphs of the orthogonality graphs. Using the technique of combinatorial designs, we also determine the quantum chromatic number of the distance-2 Hamming graph, whose edges consist of binary vectors of Hamming distance 2, for infinitely many length. |
| title | Quantum Chromatic Number of Subgraphs of Orthogonality Graphs and the Distance-2 Hamming Graph |
| topic | Combinatorics Quantum Physics 05C15, 05B30 |
| url | https://arxiv.org/abs/2512.01195 |