We obtain an explicit formula for the number of labeled connected outerplanar k-cyclic n-vertex bridgeless graphs. We find asymptotics for the number of those graphs for a large number of vertices and fixed k. As a consequence, we prove that, for k fixed, almost all labeled connected outerplanar k-cyclic graphs have bridges.

中文翻译：

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关于标记外平面k-循环无桥图的数目

我们获得了标记连接的外平面k环n顶点无桥图的数量的显式公式。对于大量的顶点和固定的k，我们发现那些图的数量是渐近的。结果，我们证明，对于固定的k个，几乎所有标记的连接外平面k环图都有桥。