Asymptotic behavior of the transition probability of a simple random walk on a line graph

Abstract

For simple random walks {P_Gⁿ} on a homogeneous graph G and {P_L(G)ⁿ} on its line graph L(G), we obtain the relationship between the asymptotic behavior of the n-step transition probability P_Gⁿ(x, x) and that of P_L(G)ⁿ(x, x) as n→∞.