Base Graph
A base graph is an underlying graph relative to which another graph construction is defined. In a graph cover p:G^~->G, the graph G is the base graph, while G^~ is the covering graph. Vertices and edges of G^~ are said to lie over their images in the base graph.
In voltage graph theory, a voltage graph is a base graph with voltages; its derived graph is a lift over that graph (roughly, a graph lying above the base graph whose vertices and edges project down to the base graph, with incident edges matching locally).
See also
Derived Graph, Graph Cover, Lift, Voltage GraphExplore with Wolfram|Alpha
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References
Gross, J. L. and Tucker, T. W. Topological Graph Theory. New York: Wiley, 1987.Cite this as:
Weisstein, Eric W. "Base Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BaseGraph.html