Covering graph
In the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to the vertex set of G. A covering map f is a surjection and a local isomorphism: the neighbourhood of a vertex v in C is mapped bijectively onto the neighbourhood of f ( v ) {\displaystyle f(v)} in G. The term lift is often used as a synonym for a covering graph of a connected graph. Though it may be misleading, there is no (obvious) relationship between covering graph and vertex cover or edge cover.