Symmetric Covers and Pseudocovers of Complete Graphs

2022/10/31 by Yan Zhou Zhu, Zhu, Yan Zhou
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2210.17118

openalex publication_date 2022/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first characterize all faithful arc-transitive covers of complete graphs and we give a general construction of such covers. For a counterpart of cover, we say a graph Γ is a pseudocover of its quotient Σ if they have the same valency and Γ is not a cover of Σ.As the second result of this paper, we prove that the complete graph \K_n has a connected arc-transitive pseudocover if and only if n-1 is not a prime.

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