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arXiv · 2210.02679

Covers and pseudocovers of symmetric graphs

Cai Heng Li·Yan Zhou Zhu
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Abstract

We introduce the concept of pseudocover, which is a counterpart of cover, for symmetric graphs. The only known example of pseudocovers of symmetric graphs so far was given by Praeger, Zhou and the first-named author a decade ago, which seems technical and hard to extend to obtain more examples. In this paper, we present a criterion for a symmetric extender of a symmetric graph to be a pseudocover, and then apply it to produce various examples of pseudocovers, including (1) with a single exception, each Praeger-Xu's graph is a pseudocover of a wreath graph; (2) each connected tetravalent symmetric graph with vertex stabilizer of size divisible by $32$ has connected pseudocovers.

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Cai Heng Li, Yan Zhou Zhu. 2022-10-06. Covers and pseudocovers of symmetric graphs. https://doi.org/10.1007/s10801-024-01324-z

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