Geodesic
Enumeration of Labeled Bicyclic and Tricyclic Eulerian Graphs
Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 678-683

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Explicit formulas for the number of labeled bicyclic and tricyclic Eulerian graphs and for the number of labeled tricyclic Eulerian blocks are obtained. Many-vertex asymptotics for these numbers are found.
Keywords: labeled Eulerian graph, bicyclic Eulerian graph, tricyclic Eulerian graph, Eulerian block, enumeration of graphs, generating function. 
@article{MZM_2012_92_5_a3,
     author = {V. A. Voblyi},
     title = {Enumeration of {Labeled} {Bicyclic} and {Tricyclic} {Eulerian} {Graphs}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {678--683},
     publisher = {mathdoc},
     volume = {92},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a3/}
}
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V. A. Voblyi. Enumeration of Labeled Bicyclic and Tricyclic Eulerian Graphs. Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 678-683. http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a3/