The aim of this paper is to present a study of the Moore–Penrose inverse [Formula: see text] of the Laplacian matrix of a simple and connected graph, particularly, for some families of graphs such as path, cycle, ladder, fan and wheel graphs. For this purpose, it is used diverse approaches and MP inverse of the Cartesian product of graphs, and are obtained new closed-form formulas of the [Formula: see text] of these families. A comparison of the computational efficiency of the new formulas versus traditional mathematical software is presented, showing the advantage of new formulas.