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Graph Arc

An arc of a graph is an ordered pair of adjacent vertices (Godsil and Royle 2001, p. 59). It is also known as a directed edge (Jones and Singerman 1978) and is sometimes called a flag (Godsil and Royle 2001, p. 59) or a directed line (Harary 1994, p. 10).

An arc-transitive graph is one whose automorphism group acts transitively on its arcs (Godsil and Royle 2001, p. 59).

See also

Arc, Arc Set, Arc-Transitive Graph, Directed Edge

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References

Godsil, C. and Royle, G. Algebraic Graph Theory. New York: Springer-Verlag, 2001.Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Jones, G. A. and Singerman, D. "Theory of Maps on Orientable Surfaces." Proc. London Math. Soc. 37, 273-307, 1978. https://doi.org/10.1112/plms/s3-37.2.273.

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Graph Arc

Cite this as:

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

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