Definition
Let G = (V, E) and C = (V2, E2) be two graphs, and let f: V2 → V be a surjection. Then f is a covering map from C to G if for each v ∈ V2, the restriction of f to the neighbourhood of v is a bijection onto the neighbourhood of f(v) ∈ V in G. Put otherwise, f maps edges incident to v one-to-one onto edges incident to f(v).
If there exists a covering map from C to G, then C is a covering graph, or a lift, of G. An h-lift is a lift such that the covering map f has the property that for every vertex v of G, its fiber f-1(v) has exactly h elements.
Read more about this topic: Covering Graph
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