Covers and Pseudocovers of Symmetric Graphs

DOI10.1007/S10801-024-01324-ZarXiv2210.02679MaRDI QIDQ6413064

Publication date: 6 October 2022

Abstract: We introduce the concept of {it pseudocover}, which is a counterpart of {it 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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