Dart

A dart in graph theory is one of the two possible orientations of an graph edge. Equivalently, a dart can be viewed as an ordered incident vertex-edge pair. For an edge e joining vertices u and v, the corresponding darts may be denoted e:u->v and e^(-1):v->u.

Darts are used in combinatorial descriptions of graph embeddings. For example, a rotation system specifies the cyclic order of the darts emanating from each graph vertex, and a voltage graph assigns a group element to each dart, with opposite darts assigned inverse group elements (Gross and Tucker 1987).

The graph-theoretic term dart should not be confused with the dart graph.

The word dart is also the name given to the Penrose tile illustrated above, with the other tile in the kite-dart pair known as the kite.

See also

Dart Graph, Graph Arc, Graph Edge, Kite, Penrose Tiles, Rotation System, Voltage Graph

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References

Gross, J. L. and Tucker, T. W. Topological Graph Theory. New York: Wiley, 1987.

Referenced on Wolfram|Alpha

Dart

Cite this as:

Weisstein, Eric W. "Dart." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Dart.html

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