The resistance distances of electrical networks based on Laplacian generalized inverse

In this paper, the generalized inverse representations for the Laplacian block matrices of graphs G1⊡G2G1⊡G2 and G1⊟G2G1⊟G2 are proposed, based on which the explicit resistance distance can be obtained for the arbitrary two-vertex resistance in the electrical networks. Moreover, some numerical examples are presented, which show the correction and efficiency of the obtained results.