Abstract
A graph Γ is said to be G-arc-regular if a subgroup G ≤ Aut(Γ) acts regularly on the arcs of Γ. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D 2n of order 2n whose cyclic subgroup C n ≤D 2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D 2n, n odd, are classified.
Original language | English |
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Pages (from-to) | 437-455 |
Number of pages | 19 |
Journal | Journal of Algebraic Combinatorics |
Volume | 38 |
Issue number | 2 |
DOIs | |
State | Published - 1 Sep 2013 |
Externally published | Yes |
Keywords
- Cayley graph
- Cayley map
- Dihedral group
- G-arc-regular graph
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics