Orientable vertex transitive embeddings of $ {{\sf K}}_p

• Published in: AIMS mathematics Vol. 8; no. 7; pp. 15024 - 15034
• Main Authors: Yu, Xue, Zhang, Qingshan
• Format: Journal Article
• Language: English
• Published: AIMS Press 01-04-2023
• Subjects: complete graphs; frobenius groups; vertex-transitive
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2023767

In [ J. Combin. Theory Ser. B , 99 (2009), 447-454)], Li characterized the classification of vertex-transitive embeddings of complete graphs, and proposed how to enumerate such maps. In this paper, we study the counting problem of orientable vertex-transitive embeddings of $ {{\sf K}}_p $, where $ p\geq 5 $ is a prime. Moreover, we obtain the number of non-isomorphic orientable vertex-transitive complete maps with $ p $ vertices.