A Large Family of Strongly Regular Graphs with Small Weisfeiler-Leman Dimension

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2025-03-24 DOI:10.1007/s00493-025-00145-3

Jinzhuan Cai, Jin Guo, Alexander L. Gavrilyuk, Ilia Ponomarenko

引用次数: 0

Abstract

In 2002, D. Fon-Der-Flaass constructed a prolific family of strongly regular graphs. In this paper, we prove that for infinitely many natural numbers n and a positive constant c, this family contains at least \(n^{c\cdot n^{2/3}}\) strongly regular n-vertex graphs X with the same parameters, which satisfy the following condition: an isomorphism between X and any other graph can be verified by the 4-dimensional Weisfeiler-Leman algorithm.

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一类具有小Weisfeiler-Leman维数的强正则图

2002年，D. Fon-Der-Flaass构造了一个多产的强正则图族。本文证明了对于无穷多个自然数n和一个正常数c，该族包含至少\(n^{c\cdot n^{2/3}}\)具有相同参数的强正则n顶点图X，满足以下条件：X与任何其他图之间的同构可以用四维Weisfeiler-Leman算法来验证。

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

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.