Hamilton cycles of semisymmetric graphs of order $2p^3$

Abstract

In light of Lov\'{a}sz's longstanding question on the existence of Hamilton paths in vertex-transitive graphs, Du and Yuan considered a natural variant: what if vertex-transitivity is relaxed, while a high degree of symmetry--specifically edge-transitivity--is retained? To investigate this, they studied semisymmetric graphs (i.e. regular, edge-transitive, but not vertex-transitive graphs) and showed that every connected semisymmetric graph of order $2pq$, where $p$ and $q$ are distinct primes, contains a Hamilton cycle. In this paper, it is shown that for any prime $p$, every connected semisymmetric graph of order $2p^3$ also contains a Hamilton cycle.