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

Xue Yu; Qingshan Zhang; Xue Yu; Qingshan Zhang

doi:10.3934/math.2023767

AIMS Mathematics

2023, Volume 8, Issue 7: 15024-15034. doi: 10.3934/math.2023767

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

Xue Yu ^,,
Qingshan Zhang

Department of Mathematics, Henan Institute of Science and Technology, Xinxiang, Henan 453003, China

Received: 07 February 2023 Revised: 27 March 2023 Accepted: 07 April 2023 Published: 23 April 2023
MSC : 20B15, 20B30, 05C25, 05C30

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.
- vertex-transitive,
- maps,
- complete graphs,
- Frobenius groups
Citation: Xue Yu, Qingshan Zhang. Orientable vertex transitive embeddings of $ {{\sf K}}_p $[J]. AIMS Mathematics, 2023, 8(7): 15024-15034. doi: 10.3934/math.2023767

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Abstract

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.

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