On the Number of Labeled Outerplanar k-Cyclic Bridgeless Graphs
Vitalii Antonievich Voblyi · Journal of Applied and Industrial Mathematics · 2020
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.