Orientable Vertex Transitive Embeddings of Complete Graphs Kp2

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.