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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.02679 |
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| _version_ | 1866909418573004800 |
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| author | Li, Cai Heng Zhu, Yan Zhou |
| author_facet | Li, Cai Heng Zhu, Yan Zhou |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02679 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Covers and pseudocovers of symmetric graphs Li, Cai Heng Zhu, Yan Zhou Combinatorics Group Theory 20B25, 05C25 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. |
| title | Covers and pseudocovers of symmetric graphs |
| topic | Combinatorics Group Theory 20B25, 05C25 |
| url | https://arxiv.org/abs/2210.02679 |