Strongly regular Cayley graphs from partitions of subdifference sets of the Singer difference sets
Strongly regular Cayley graphs from partitions of subdifference sets of the Singer difference sets
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DOI：
10.1016/j.ffa.2017.11.010
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
K. Momihara;Qing Xiang
中科院分区：
文献类型：
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作者：
K. Momihara;Qing Xiang
本文给出了强正则Cayley图的一种新的“双曲”型提升结构。基于Singer差集的次差集的划分，我们给出了有限域的加性群上强正则Cayley图的新构造。我们的结果统一了有限几何中与双卵形和紧集相关的强正则Cayley图的一些最新构造。此外，本文得到的一些强正则Cayley图是新的或不同构于已知的具有相同参数的强正则图。
In this paper, we give a new lifting construction of “hyperbolic” type of strongly regular Cayley graphs. Also we give new constructions of strongly regular Cayley graphs over the additive groups of finite fields based on partitions of subdifference sets of the Singer difference sets. Our results unify some recent constructions of strongly regular Cayley graphs related tom-ovoids andi-tight sets in finite geometry. Furthermore, some of the strongly regular Cayley graphs obtained in this paper are new or nonisomorphic to known strongly regular graphs with the same parameters.