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Weak metacirculants of odd prime power order
- Source :
- Journal of Combinatorial Theory, Series A 155 (2018) 225-243
- Publication Year :
- 2016
-
Abstract
- Metacirculants are a basic and well-studied family of vertex-transitive graphs, and weak metacirculants are generalizations of them. A graph is called a weak metacirculant if it has a vertex-transitive metacyclic automorphism group. This paper is devoted to the study of weak metacirculants with odd prime power order. We first prove that a weak metacirculant of odd prime power order is a metacirculant if and only if it has a vertex-transitive split metacyclic automorphism group. We then prove that for any odd prime $p$ and integer $\ell\geq 4$, there exist weak metacirculants of order $p^\ell$ which are Cayley graphs but not Cayley graphs of any metacyclic group; this answers a question in Li et al. (2013). We construct such graphs explicitly by introducing a construction which is a generalization of generalized Petersen graphs. Finally, we determine all smallest possible metacirculants of odd prime power order which are Cayley graphs but not Cayley graphs of any metacyclic group.
- Subjects :
- Mathematics - Combinatorics
05C25, 20B25
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Combinatorial Theory, Series A 155 (2018) 225-243
- Publication Type :
- Report
- Accession number :
- edsarx.1611.06264
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jcta.2017.11.007