05963796

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05963796 Wan, Liangxia Liu, Yanpei Orientable embedding distributions by genus for certain type of non-planar graphs. II. Ars Comb. 94, 201-210 (2010). 2010 Charles Babbage Research Centre, Winnipeg, MB EN embedding distribution joint tree surface genus Zbl 1141.05319 Summary: In this paper we give an explicit expression of the genus distributions of $M^n_j$, for $j=1,2,\dots ,11$, which are introduced in the authors' previous paper [``Orientable embedding distributions by genus for certain type of non-planar graphs. I,'' Ars Comb. 79, 97--105 (2006; Zbl 1141.05319)]. For a connected graph $G=(V,E)$ with a cycle, let $e$ be an edge on a cycle. By adding $2n$ vertices $u_1$, $u_2$, $u_3$, \dots , $u_n$, $v_1$, $v_2$, $v_3$, \dots , $v_n$ on $e$ in sequence and connecting $u_k v_k$- for $k$, $1\le k\le n$, a non-planar graph $G_n$ is obtained for $n\ge 3$. Thus, the orientable embedding distribution of $G_n$ by genus is obtained via the genus distributions of $M^n_j$.