The Number of Labeled Outerplanar k-Cyclic Graphs
Vitalii Antonievich Voblyi · Mathematical Notes · 2018
A k -cyclic graph is a graph with cyclomatic number k . An explicit formula for the number of labeled connected outerplanar k -cyclic graphs with a given number of vertices is obtained. In addition, such graphs with fixed cyclomatic number k and a large number of vertices are asymptotically enumerated. As a consequence, it is found that, for fixed k , almost all labeled connected outerplanar k -cyclic graphs with a large number of vertices are cacti.