We study nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and the Johnson graphs. For the first eigenvalue we obtain the minimums of $L_{\infty}$-norm for several infinite series of Johnson graphs, including J(n,3) as well as general upper and lower bounds. The minimization of $L_{\infty}$-norm for nowhere-zero integer eigenvectors with the second eigenvalue of the block graph of a Steiner triple system $S$ is equivalent to finding the minimum nowhere-zero flow for Steiner triple system S. For the all Assmuss-Mattson Steiner triple systems of order at least 99 we prove that this minimum is bounded above by 4.

翻译：我们研究施泰纳三元系的分块图与约翰逊图中的无处零整数特征向量。针对第一特征值，我们获得了多个无穷约翰逊图序列（包括J(n,3)）的$L_{\infty}$范数最小值，并给出了通用的上下界。对于施泰纳三元系$S$的分块图，其第二特征值对应无处零整数特征向量的$L_{\infty}$范数最小化问题，等价于寻找施泰纳三元系$S$的最小无处零流。对于阶数至少为99的所有Assmuss-Mattson施泰纳三元系，我们证明该最小值的上界为4。