Every finite non-abelian group admits a non-Cayley Haar graph, except the dihedral groups of orders 6, 8, and 10, the quaternion group Q8, and Q8 × Z2.
On cubic symmetric non-Cayley graphs with solvable automorphism groups
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
It was proved in [Y.-Q. Feng, C. H. Li and J.-X. Zhou, Symmetric cubic graphs with solvable automorphism groups, {\em European J. Combin.} {\bf 45} (2015), 1-11] that a cubic symmetric graph with a solvable automorphism group is either a Cayley graph or a $2$-regular graph of type $2^2$, that is, a graph with no automorphism of order $2$ interchanging two adjacent vertices. In this paper an infinite family of non-Cayley cubic $2$-regular graphs of type $2^2$ with a solvable automorphism group is constructed. The smallest graph in this family has order 6174.
fields
math.CO 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Existence of non-Cayley Haar graphs
Every finite non-abelian group admits a non-Cayley Haar graph, except the dihedral groups of orders 6, 8, and 10, the quaternion group Q8, and Q8 × Z2.