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
Famous quotes containing the word definition:
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)