In 2022, the second author found a prolific construction of strongly regular graphs, which is based on joining a coclique and a divisible design graph with certain parameters. The construction produces strongly regular graphs with the same parameters as the complement of the symplectic graph \(\textsf{Sp}(2d,q)\). In this paper, we determine the parameters of strongly regular graphs which admit a decomposition into a divisible design graph and a coclique attaining the Hoffman bound. In particular, it is shown that when the least eigenvalue of such a strongly regular graph is a prime power, its parameters coincide with those of the complement of \(\textsf{Sp}(2d,q)\). Furthermore, a generalization of the construction is discussed.

2022 年，第二作者发现了一种多产的强正则图构造，该构造基于将 coclique 和具有某些参数的可除设计图连接起来。该构造生成具有与辛图补集相同参数的强正则图\(\textsf{Sp}(2d,q)\)。在本文中，我们确定了强正则图的参数，该图允许分解为可分设计图和达到霍夫曼界的尾翼。特别是，当这种强正则图的最小特征值是素数幂时，其参数与\(\textsf{Sp}(2d,q)\)的补集的参数一致。此外，还讨论了该结构的一般化。