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- W2971042716 abstract "The bouquet of circles $B_n$ and dipole graph $D_n$ are two important classes of graphs in topological graph theory. For $ngeq 1$, we give an explicit formula for the average genus $gamma_{avg}(B_n)$ of $B_n$. By this expression, one easily sees $gamma_{avg}(B_n)=frac{n-ln n-c+1-ln 2}{2}+o(1)$, where $c$ is the Euler constant. Similar results are obtained for $D_n$. Our method is new and deeply depends on the knowledge in ordinary differential equations." @default.
- W2971042716 created "2019-09-05" @default.
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- W2971042716 date "2019-08-30" @default.
- W2971042716 modified "2023-09-26" @default.
- W2971042716 title "The average genus for bouquets of circles and dipoles" @default.
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- W2971042716 doi "https://doi.org/10.48550/arxiv.1908.11544" @default.
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