论小型严格诺伊迈尔图的存在

Pub Date : 2024-04-08 DOI:10.1007/s00373-024-02779-4

Aida Abiad, Maarten De Boeck, Sjanne Zeijlemaker

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引用次数: 0

摘要

Neumaier 图是包含一个规则小块的非完整边规则图。在这项工作中，我们证明了关于小型严格 Neumaier 图存在性的几个结果。特别是，我们从理论上证明了参数为 (16, 9, 4; 2, 4) 的最小严格 Neumaier 图的唯一性；我们建立了参数为 (25, 12, 5. 2, 5) 的严格 Neumaier 图的存在性；我们反驳了参数为 (16, 9, 4; 2, 4) 的最小严格 Neumaier 图的唯一性；2，5），并反证了参数为 (25, 16, 9; 3, 5)、(28, 18, 11; 4, 7)、(33, 24, 17; 6, 9)、(35, 2212; 3, 5)、(40, 30, 22; 7, 10) 和 (55, 34, 18; 3, 5) 的严格诺伊迈尔图的存在性。我们的证明使用了组合技术和新颖的整数编程方法。

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On the Existence of Small Strictly Neumaier Graphs

A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this work, we prove several results on the existence of small strictly Neumaier graphs. In particular, we present a theoretical proof of the uniqueness of the smallest strictly Neumaier graph with parameters (16, 9, 4; 2, 4), we establish the existence of a strictly Neumaier graph with parameters (25, 12, 5; 2, 5), and we disprove the existence of strictly Neumaier graphs with parameters (25, 16, 9; 3, 5), (28, 18, 11; 4, 7), (33, 24, 17; 6, 9), (35, 2212; 3, 5), (40, 30, 22; 7, 10) and (55, 34, 18; 3, 5). Our proofs use combinatorial techniques and a novel application of integer programming methods.

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