Orientable Embedding Genus Distributions for a Graph with a Certain Type of Ladders

Liangxia Wan
Department of Mathematics, Northern Jiaotong University, Beijing 100074, P. R. China


Abstract     Full Text  DVI

In this paper the genus distribution of some basic surface sets are computed. Let $G$ be a connected graph. A graph $G_n$ is obtained by adding $n$ parallel edges $a_l$ on edges $e_1$ and $e_2$ of $G$ such that the ends of $a_l$ are on $e_1$ and $e_2$ each for a positive integer $n$, $1\leq l\leq n$. Embedding surfaces are extracted by using the joint trees of a graph. By using surface sorting method we get the orientable embedding distribution polynomial of $G_n$. As a special consequence, the orientable embedding distributions of closed-end ladders, Ringel ladders, circular ladders and M\"{o}bius ladders by their genera are simply deduced.