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<p>A regular Cayley map is a 2-cell embedding of a Cayley graph into a closed orientable surface whose orientation-preserving automorphism group acts regularly on the set of all incident vertex-edge pairs, while a regular generalized Cayley map is a 2-cell embedding of a Cayley graph into a closed (orientable or nonorientable) surface whose automorphism group acts regularly on the set of all incident vertex–edge–face triples. Recently, regular Cayley maps over elementary abelian <i>p</i>-groups are classified in [<CitationRef CitationID="CR6">6</CitationRef>]. A nature question is to classify regular generalized Cayley maps over them. In this paper, a complete classification is given.</p>

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Regular generalized cayley maps of elementary abelian p-groups

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Hao Yu

摘要

A regular Cayley map is a 2-cell embedding of a Cayley graph into a closed orientable surface whose orientation-preserving automorphism group acts regularly on the set of all incident vertex-edge pairs, while a regular generalized Cayley map is a 2-cell embedding of a Cayley graph into a closed (orientable or nonorientable) surface whose automorphism group acts regularly on the set of all incident vertex–edge–face triples. Recently, regular Cayley maps over elementary abelian p-groups are classified in [6]. A nature question is to classify regular generalized Cayley maps over them. In this paper, a complete classification is given.