Edge-transitive dihedral or cyclic covers of cubic symmetric graphs of order \(2p\)
Let \(X=(V(X),E(X))\) be a finite connected undirected graph. Then, a sequence \(\{v_0,v_1,\dots,v_s\}\) of vertices of \(X\) such that \(\{v_{i-1},v_i\}\in E\) for all \(i=1,2,\dots,s\) and \(v_{i-1}\neq v_{i+1}\) for all \(i=1,2,\dots,s-1\) is called an \(s\)-arc of \(X\). An epimorphism \(\phi :\tilde {X}\to X\) of graphs is called a regular covering projection if there exists a semiregular subgroup \(\mathrm{CT}(\phi)\) of the automorphism group of \(X\) such that the orbits of \(\mathrm{CT}(\phi)\) coincide with fibres \(\phi^{-1}(v)\), \(v\in V(X)\), the arc orbits of \(\mathrm{CT}(\phi)\) coincide with the arc fibres and the edge orbits of \(\mathrm{CT}(\phi)\) coincide with the edge fibres. If \(\mathrm{CT}(\phi)\) is isomorphic to an abstract group \(G\) then \(\tilde {X}\) is called \(G\)-cover of \(X\). The paper classifies, up to isomorphism, edge transitive cyclic (and/or dihedral) covers of a cubic symmetric graph \(X\) of order \(2p\) where \(p\) is a prime.
scientific article; zbMATH DE number 6330533
scientific article