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Enumeration reveals orientable vertex-transitive embeddings in complete graphs, suggesting new mapping applications.
This paper investigates the enumeration of orientable vertex-transitive embeddings of complete graphs Kp2, where p≥5 is a prime. Building on the classification framework established by Li, we derive a precise count of these embeddings up to non-isomorphism. Furthermore, we provide explicit examples to demonstrate the realizability of the maps corresponding to our enumeration results.
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Yu et al. (2026) studied this question.
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