On Hamilton Paths in Vertex-Transitive Graphs of Order 10p

Shaofei Du, Wenjuan Luo, Hao Yu

Abstract: It was shown by Kutnar, Marušič and Zhang in 2012 that every connected vertex-transitive graph of order 10p, where p is a prime and \(p\ne 7\), contains a Hamilton path, except for graphs X arising from the action of \(\textrm{PSL}(2, s^m)\) on cosets of \(\mathbb {Z}_s^m\rtimes \mathbb {Z}_{\frac{s^m-1}{10}}\), where s is a prime. In this paper, Hamilton cycles of these exceptions X will be found.