Abstract: A step forward is made in a long standing Lovász problem regarding hamiltonicity of vertex-transitive graphs by showing that every connected vertex-transitive graph of order a product of two primes arising from the group action of the projective special linear group PSL▫$(2, q^2)$▫ on cosets of its subgroup isomorphic to the projective general linear group PGL$(2, q)$ contains a Hamilton cycle.Keywords: vertex-transitive graph, Hamilton cycle, automorphism group, orbital graphPublished in RUP: 20.07.2020; Views: 1412; Downloads: 46 Full text (365,31 KB)