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On G-arc-regular dihedrants and regular dihedral maps |
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| Authors: | István Kovács Dragan Marušič Mikhail Muzychuk |
| Institution: | 1. FAMNIT, University of Primorska, Glagolja?ka 8, 6000, Koper, Slovenia 2. PEF, University of Ljubljana, Kardeljeva pl. 16, 1000, Ljubljana, Slovenia 3. Department of Computer Science and Mathematics, Netanya Academic College, University st. 1, 42365, Netanya, Israel |
| Abstract: | A graph Γ is said to be G-arc-regular if a subgroup $G \le\operatorname{\mathsf{Aut}}(\varGamma)$ 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. |
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