Symmetric Covers and Pseudocovers of Complete Graphs

Publication date: 31 October 2022

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

G a m m a

is a pseudocover of its quotient

S i g m a

if they have the same valency and

G a m m a

is not a cover of

S i g m a

.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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