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Research Article | Open Access

Orientable vertex transitive embeddings of K p

Xue Yu( ), Qingshan Zhang
Department of Mathematics, Henan Institute of Science and Technology, Xinxiang, Henan 453003, China
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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 K p , where p ≥ 5 is a prime. Moreover, we obtain the number of non-isomorphic orientable vertex-transitive complete maps with p vertices.

Keywords

vertex-transitivemapscomplete graphsFrobenius groups
CLC number: 20B15, 20B30, 05C25, 05C30

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 15024-15034
DOI: 10.3934/math.2023767

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Cite this article:
Yu X, Zhang Q. Orientable vertex transitive embeddings of K p . AIMS Mathematics, 2023, 8(7): 15024-15034. https://doi.org/10.3934/math.2023767

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Received: 07 February 2023
Revised: 27 March 2023
Accepted: 07 April 2023
Published: 15 July 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)