In this paper, we show that Graph Isomorphism (GI) is not $\textsf{AC}^{0}$-reducible to several problems, including the Latin Square Isotopy problem, isomorphism testing of several families of Steiner designs, and isomorphism testing of conference graphs. As a corollary, we obtain that GI is not $\textsf{AC}^{0}$-reducible to isomorphism testing of Latin square graphs and strongly regular graphs arising from special cases of Steiner $2$-designs. We accomplish this by showing that the generator-enumeration technique for each of these problems can be implemented in $\beta_{2}\textsf{FOLL}$, which cannot compute Parity (Chattopadhyay, Tor\'an, & Wagner, ACM Trans. Comp. Theory, 2013).

翻译：本文证明图同构（GI）问题不能通过$\textsf{AC}^{0}$归约转化为若干问题，包括拉丁方同痕问题、若干斯坦纳设计族的同构判定问题以及会议图的同构判定问题。作为推论，我们得到GI不能通过$\textsf{AC}^{0}$归约转化为拉丁方图的同构判定问题以及由特殊斯坦纳$2$-设计导出的强正则图的同构判定问题。我们通过证明这些问题的生成元枚举技术可在$\beta_{2}\textsf{FOLL}$中实现来完成上述结论，而该复杂度类无法计算奇偶性问题（Chattopadhyay, Tor\'an, & Wagner, ACM Trans. Comp. Theory, 2013）。