Let \(H_G(x, y)\) be the expected hitting time from vertex x to vertex y for the first time on a simple connected graph G and \(\varphi (G){:}{=}\max \left\{ H_G(x, y): x, y\in V(G)\right\}\) be called the hitting time of G. In this paper, sharp upper and lower bounds for \(\varphi (G)\) among all n-vertex bicyclic graphs are presented and the extremal graphs are determined.

中文翻译：

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双环图上随机游走的命中次数

设\(H_G(x, y)\)是在简单连通图G上第一次从顶点x到顶点y的预期命中时间和\(\varphi (G){:}{=}\max \left \{ H_G(x, y): x, y\in V(G)\right\}\)称为G的命中时间。在本文中，给出了所有n顶点双环图中\(\varphi (G)\) 的尖锐上下界，并确定了极值图。