Cayley maps
Cayley maps
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DOI：
10.1016/j.jctb.2005.04.007
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发表时间：
2005-11
期刊：
影响因子：
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通讯作者：
R. Richter;J. Širáň;R. Jajcay;Thomas W. Tucker;Mark E. Watkins
中科院分区：
文献类型：
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作者：
R. Richter;J. Širáň;R. Jajcay;Thomas W. Tucker;Mark E. Watkins
我们提出了Cayley图的理论，即将Cayley图嵌入到每个顶点周围具有相同循环旋转的生成器的有向曲面中。这些映射经常被用来编码图的对称嵌入。我们还提出了Cayley映射的代数理论，并应用该理论精确地确定球体或平面的规则或边传递平铺是Cayley映射或Cayley图。然而，我们的主要目标是提供一般理论，以便使其他人更容易研究凯利图。
We present a theory of Cayley maps, i.e., embeddings of Cayley graphs into oriented surfaces having the same cyclic rotation of generators around each vertex. These maps have often been used to encode symmetric embeddings of graphs. We also present an algebraic theory of Cayley maps and we apply the theory to determine exactly which regular or edge-transitive tilings of the sphere or plane are Cayley maps or Cayley graphs. Our main goal, however, is to provide the general theory so as to make it easier for others to study Cayley maps.