Random walks on the folded hypercube

Random walks are basic mechanism for many dynamic processes on the network. In this paper, we study the global mean first-passage time (GMFPT) of random walks on the n-dimensional folded hypercube FQ_n. FQ_n is a variation of the hypercube Q_n by adding complementary edges, and characterized with the superiorities of smaller diameter and higher connectivity than the hypercube. We initiate a more concise formula to the Kirchhoff index by using the spectra of the Laplace matrix of FQ_n. We also obtain the explicit formula to GMFPT, and the exponent of scaling efficiency characterizing the random walks is further determined, finding that it takes less time when random walks on FQ_n than on Q_n. Moreover, we explore random walks on the FQ_n considering a given trap. Finally, we make some comparison with Q_n in Kirchhoff index, noticing a more effective traffic on FQ_n.