Geodesic
Enumeration of labeled series-parallel tricyclic graphs
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 177 (2020), pp. 132-136

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A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. An explicit formula for the number of labeled series-parallel tricyclic graphs with a given number of vertices is obtained, and the corresponding asymptotics for the number of such graphs with a large number of vertices is found. We prove that under a uniform probability distribution, the probability that the labeled tricyclic graph is a series-parallel graph is asymptotically equal to $13/15$.
Keywords: enumeration, labeled graph, series-parallel graph, asymptotics, probability. 
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     author = {V. A. Voblyi},
     title = {Enumeration of labeled series-parallel tricyclic graphs},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {132--136},
     publisher = {mathdoc},
     volume = {177},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_177_a14/}
}
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V. A. Voblyi. Enumeration of labeled series-parallel tricyclic graphs. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 177 (2020), pp. 132-136. http://geodesic.mathdoc.fr/item/INTO_2020_177_a14/