Let \(L_G\) be the Laplacian matrix of a graph G with n vertices, and let \({\mathbf {b}}\) be a binary vector of length n. The pair \((L_G, {\mathbf {b}})\) is said to be controllable (and we also say that G is Laplacian controllable for \({\mathbf {b}}\)) if \(L_G\) has no eigenvector orthogonal to \({\mathbf {b}}\). In this paper we study the Laplacian controllability of joins, Cartesian products, tensor products and strong products of two graphs. Besides some theoretical results, we give an iterative construction of infinite families of controllable pairs \((L_G, {\mathbf {b}})\).

令\（L_G \）是具有n个顶点的图G的拉普拉斯矩阵，而令\（{\ mathbf {b}} \）是长度为n的二元向量。该对\（（L_G，{\ mathbf {B}}）\）被说成是可控制的（和我们也说ģ为拉普拉斯可控\（{\ mathbf {B}} \） ）如果\（L_G \ ）没有正交于\（{\ mathbf {b}} \）的特征向量。在本文中，我们研究了两个图的连接，笛卡尔积，张量积和强积的拉普拉斯可控性。除了一些理论结果，我们给出了可控对的无限族的迭代构造\（（L_G，{\ mathbf {b}}）\）。