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The Adjacency Codes of the First Yellow Graphs
Journal of Systems Science and Complexity ( IF 2.1 ) Pub Date : 2023-08-23 , DOI: 10.1007/s11424-023-1518-0
Minjia Shi , Shitao Li , Jon-Lark Kim , Patrick Solé

The authors study the binary codes spanned by the adjacency matrices of the strongly regular graphs (SRGs) on at most two hundred vertices whose existence is unknown. The authors show that in length less than one hundred they cannot be cyclic, except for the exceptions of the SRGs of parameters (85, 42, 20, 21) and (96, 60, 38, 36). In particular, the adjacency code of a (85,42, 20, 21) is the zero-sum code. In the range [100, 200] the authors find 29 SRGs that could possibly have a cyclic adjacency code.



中文翻译:

第一个黄色图的邻接码

作者研究了强正则图 (SRG) 的邻接矩阵所跨越的二进制代码,最多有 200 个未知顶点。作者表明,除了参数 (85, 42, 20, 21) 和 (96, 60, 38, 36) 的 SRG 之外,长度小于 100 的它们不能是循环的。特别地,a(85,42,20,21)的邻接码是零和码。在 [100, 200] 范围内,作者发现 29 个 SRG 可能具有循环邻接码。

更新日期:2023-08-23
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