Geodesic
The Number of Labeled Outerplanar $k$-Cyclic Graphs
Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 657-666

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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.
Keywords: enumeration, labeled graph, connected graph, $k$-cyclic graph, outerplanar graph, asymptotics.
Mots-clés : cactus 
@article{MZM_2018_103_5_a1,
     author = {V. A. Voblyi},
     title = {The {Number} of {Labeled} {Outerplanar} $k${-Cyclic} {Graphs}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {657--666},
     publisher = {mathdoc},
     volume = {103},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a1/}
}
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V. A. Voblyi. The Number of Labeled Outerplanar $k$-Cyclic Graphs. Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 657-666. http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a1/