Generalized Gardiner–Praeger graphs and their symmetries

A subgroup of the automorphism group a graph acts half-arc-transitively on if it transitively vertex-set and edge-set but not arc-set graph. If full half-arc-transitively, is said to be half-arc-transitive. In 1994 Gardiner Praeger introduced two families tetravalent arc-transitive graphs, called C±1 C±ε that play prominent role in characterization graphs admitting an automorphisms with normal elementary abelian such corresponding quotient cycle. All Gardiner–Praeger are admit half-arc-transitive automorphisms. Quite recently, Potočnik Wilson family CPM which generalizations graphs. Most these arc-transitive, some them fact, at least up order 1000, each loosely-attached odd radius having vertex-stabilizers greater than 2 isomorphic this paper we determine investigate isomorphisms between them. Moreover, 2-arc-transitive,