New strongly regular graphs from orthogonal groups O+(6, 2) and O-(6, 2)
New strongly regular graphs from orthogonal groups O+(6, 2) and O-(6, 2)
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来自正交群 O (6, 2) 和 O-(6, 2) 的新强正则图
DOI：
10.1016/j.disc.2018.06.029
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发表时间：
2016
影响因子：
0.8
通讯作者：
Andrea Švob
中科院分区：
文献类型：
--
作者：
D. Crnković;Sanja Rukavina;Andrea Švob
证明了参数为（216，40，4，8）和（540，187，58，68）的强正则图的存在性。我们还构造了一个参数为（540，224，88，96）的强正则图，这是以前未知的。进一步，我们构造了所有顶点数不超过600的距离正则图，允许正交群O+（6，2）或O-（6，2）的传递作用。进一步证明了在一定条件下，强正则图Γ的轨道矩阵M可以用来定义一个新的强正则图Γ π，其中图Γ π的顶点对应于图Γ的轨道（M的行）.我们发现，一些得到的强正则图是相互关联的方式，可以从一个轨道矩阵的其他构造。
We prove the existence of strongly regular graphs with parameters (216, 40, 4, 8) and (540, 187, 58, 68). We also construct a strongly regular graph with parameters (540, 224, 88, 96) that was previously unknown. Further, we construct all distance-regular graphs with at most 600 vertices, admitting a transitive action of the orthogonal group O+(6, 2) or O−(6, 2). Furthermore, we show that under certain conditions an orbit matrix M of a strongly regular graph Γ can be used to define a new strongly regular graph Γ˜, where the vertices of the graph Γ˜ correspond to the orbits of Γ (the rows of M). We show that some of the obtained strongly regular graphs are related to each other in a way that one can be constructed from an orbit matrix of the other.