参数为 $λ=1$ 和 $μ=2$ 的强正则图中六角形数量的下限

arXiv - MATH - Combinatorics Pub Date : 2024-09-16 DOI:arxiv-2409.10620

Reimbay Reimbayev

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引用次数: 0

摘要

数十年来，$srg(99,14,1,2)$ 的存在一直是一个令人感兴趣的问题。在本文中，我们考虑了参数为 $\lambda =1$ 和 $\mu =2$ 的强规则图系的一般结构性质。特别是，我们建立了六边形个数的下界，并以此说明了上述图的存在性与其六边形个数之间的联系。

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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The Lower Bound for Number of Hexagons in Strongly Regular Graphs with Parameters $λ=1$ and $μ=2$

The existence of $srg(99,14,1,2)$ has been a question of interest for several decades to the moment. In this paper we consider the structural properties in general for the family of strongly regular graphs with parameters $\lambda =1$ and $\mu =2$. In particular, we establish the lower bound for the number of hexagons and, by doing that, we show the connection between the existence of the aforementioned graph and the number of its hexagons.

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arXiv - MATH - Combinatorics

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