Examples
In the following figure, the graph C is a covering graph of the graph H.
The covering map f from C to H is indicated with the colours. For example, both blue vertices of C are mapped to the blue vertex of H. The map f is a surjection: each vertex of H has a preimage in C. Furthermore, f maps bijectively each neighbourhood of a vertex v in C onto the neighbourhood of the vertex f(v) in H.
For example, let v be one of the purple vertices in C; it has two neighbours in C, a green vertex u and a blue vertex t. Similarly, let v′ be the purple vertex in H; it has two neighbours in H, the green vertex u′ and the blue vertex t′. The mapping f restricted to {t, u, v} is a bijection onto {t′, u′, v′}. This is illustrated in the following figure:
Similarly, we can check that the neighbourhood of a blue vertex in C is mapped one-to-one onto the neighbourhood of the blue vertex in H:
Read more about this topic: Covering Graph
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