On the Existence of Small Strictly Neumaier Graphs

IF 0.6 4区数学 Q3 MATHEMATICS

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

Aida Abiad, Maarten De Boeck, Sjanne Zeijlemaker

引用次数: 0

Abstract

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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论小型严格诺伊迈尔图的存在

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Graphs and Combinatorics 数学-数学

CiteScore

1.00

自引率

14.30%

发文量

160

审稿时长

6 months

期刊介绍： Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.