Maximum hitting time of random walks on unicyclic graphs with given diameter

Abstract

We explore the extremal problems of the hitting time of unicyclic graphs on n vertices with a given diameter. Let HG(u,v) be the expected hitting time from vertex u to vertex v on a simple graph G. Let φ(G) = maxu,v∈V(G)HG(u,v) be the hitting time of G. In this paper, we obtain the upper bound for the hitting time of unicyclic graphs with a given diameter, and the extremal graph that attached the value is determined.