Regular Graph Cover

A regular graph cover is a graph cover p:G^~->G whose deck transformations act transitively on each fiber of the graph projection. Equivalently, if u^~ and v^~ are two lifts of the same vertex v of G, then some deck transformation sends u^~ to v^~. Here "regular" describes the covering action, not the equality of vertex degrees in a regular graph.

Ordinary voltage graphs construct regular graph covers. More generally, permutation voltage assignments construct arbitrary graph covers (Gross and Tucker 1977, Gross and Tucker 1987).

See also

Deck Transformation, Fiber, Graph Cover, Graph Projection, Regular Graph, Transitive Group Action, Voltage Graph

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References

Gross, J. L. and Tucker, T. W. "Generating All Graph Coverings by Permutation Voltage Assignments." Disc. Math. 18, 273-283, 1977.Gross, J. L. and Tucker, T. W. Topological Graph Theory. New York: Wiley, 1987.

Cite this as:

Weisstein, Eric W. "Regular Graph Cover." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RegularGraphCover.html

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