Name
Abstract | ||
|---|---|---|
A Cayley graph of a group H is a finite simple graph Γ such that its automorphism group Aut(Γ) contains a subgroup isomorphic to H acting regularly on V(Γ), while a Haar graph of H is a finite simple bipartite graph Σ such that Aut(Σ) contains a subgroup isomorphic to H acting semiregularly on V(Σ) and the H-orbits are equal to the partite sets of Σ. It is well-known that every Haar graph of finite abelian groups is a Cayley graph. In this paper, we prove that every finite non-abelian group admits a non-Cayley Haar graph except the dihedral groups D6, D8, D10, the quaternion group Q8 and the group Q8×Z2. This answers an open problem proposed by Estélyi and Pisanski in 2016. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.ejc.2020.103146 | European Journal of Combinatorics |
DocType | Volume | ISSN |
Journal | 89 | 0195-6698 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yan-quan Feng | 1 | 350 | 41.80 |
| Kovács István | 2 | 0 | 0.34 |
| Jie Wang | 3 | 113 | 9.82 |
| Da-Wei Yang | 4 | 0 | 1.35 |