Genera of Cayley maps

Jian Bing Liu
Beijing Jiaotong University

Jin Ho Kwak
Beijing Jiaotong University

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Minisymposium: GRAPH IMBEDDINGS AND MAP SYMMETRIES

Content: The genus distribution of a graph $G$ is defined to be the sequence ${g_m}$, where $g_m$ is the number of different embeddings of $G$ in the closed orientable surface of genus $m$. In this paper, we examine the genus distribution of Cayley maps for several Cayley graphs. It will be shown that the genus distribution of Cayley maps has many different properties from its usual genus distribution.

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