Geodesic
The average genus for bouquets of circles and dipoles
Ars Mathematica Contemporanea, Tome 20 (2021) no. 2, pp. 199-208.

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The bouquet of circles Bn and dipole graph Dn are two important classes of graphs in topological graph theory. For n ≥ 1, we give an explicit formula for the average genus γavg(Bn) of Bn. By this expression, one easily sees γavg(Bn) = (n − ln n − γ + 1 − ln 2) / 2 + o(1), where γ is the Euler-Mascheroni constant. Similar results are obtained for Dn. Our method mainly depends on the technique of generating series and the knowledge in ordinary differential equations.
DOI : 10.26493/1855-3974.2043.fbb
Keywords: Average genus, bouquet of circles, dipole, ordinary differential equation 
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Jinlian Zhang; Xuhui Peng; Yichao Chen. The average genus for bouquets of circles and dipoles. Ars Mathematica Contemporanea, Tome 20 (2021) no. 2, pp. 199-208. doi : 10.26493/1855-3974.2043.fbb. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2043.fbb/

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