There are only two kinds of non-isomorphic consecutive vertex labelings of octahedron, and each of them can be deduced from the other. There is an algorithm to construct consecutive edge labelings. It is shown that there exist many non-isomorphic complementary consecutive edge labelings of octahedron.
Citation
Qu Anjing. On Complementary Consecutive Labelings of Octahedron[J], Ars Combinatoria, Volume 051. 287-294. .