AI 中文总结
本文提出将有限域乘法群的陪集两两组合的思路，发现存在可分解为彼得森图的无限序列佩利图，还构造出参数为(50,21,8,9)的新强正则图。
AI 中文摘要
本文采用一个极为简单的思路：在有限域F_q的乘法群中，考虑某个子群的陪集，并尝试将这些陪集两两组合，使得在对应的佩利图中形成的诱导子图是强正则图。研究表明，存在无限多个佩利图可按此方式分解为彼得森图。此外，利用该方法构造出了一个具有参数(50, 21, 8, 9)的新强正则图。
英文摘要
This paper utilizes an extremely simple idea: in the multiplicative group of a finite field $F_q$, cosets of a certain subgroup are considered, and an attempt is made to combine these cosets into pairs such that the resulting induced subgraph in the corresponding Paley graph is strongly regular. It is shown that there exists an infinite sequence of Paley graphs that can be partitioned into Petersen graphs in this manner. Furthermore, a new strongly regular graph with parameters $(50, 21, 8, 9)$ is constructed using this method.
Comments9 pages, 1 figure
