After long-term efforts, the Hamilton path (cycle) problem for connected vertex-transitive graphs of order pq (where p and q are primes) was finally resolved in 2021, see 10. Fifteen years ago, mathematicians began addressing this problem for graphs of order 2pq. Among these studies, it was proved in 2012 (see 21) that every connected vertex-transitive graph of order 10p (where p 7 is a prime) contains a Hamilton path, with the exception of a family of graphs that was recently confirmed in 11. In this paper, we achieve a further result: every connected vertex-transitive graph of order 10p (where p is a prime) contains a Hamilton cycle, except for the truncation of the Petersen graph.
Chen et al. (Tue,) studied this question.