Abstract
The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of.. is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks Q(n) by utilizing spectral graph theory. Moreover, we obtained the relationship of Kirchhoff index between hypercubes networks Q(n) and its three variant networks l(Q(n)), s(Q(n)), t(Q(n)) by deducing the characteristic polynomial of the Laplacian matrix related networks. Finally, the special formulae for the Kirchhoff indexes of l(Q(n)), s(Q(n)), and t(Q(n)) were proposed, respectively.