Maximal hitting times for random walks on bicyclic graphs with given number of pendant vertices

Abstract

Let HG(x, y) be the expected hitting time from vertex x to vertex y for the first
time on a simple connected graph G and φ(G) = maxx,y∈V (G)HG(x, y). Let G
tn be the set of simple connected graphs with n vertices and t pendant vertices. In this paper, we proved the upper bound of the φ(G) for G ∈ Gtn and determined the extremal graph in all n-vertex bicyclic graphs with given t pendant vertices.