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Path

A path gamma in a topological space X is a continuous map gamma:[a,b]->X, where a<b are real numbers. The points gamma(a) and gamma(b) are the initial and final points. A path parametrized by t is commonly denoted sigma(t).

A graph path is a sequence {x_1,x_2,...,x_n} such that (x_1,x_2), (x_2,x_3), ..., (x_(n-1),x_n) are graph edges of the graph and the x_i are distinct.

A common choice is [a,b]=[0,1]. The name path is also used for the image of such a continuous map.

See also

Arc, Contour, Curve, Eulerian Path, Graph, Graph Cycle, Graph Path, Hamiltonian Path, Path Graph, Pathwise-Connected, Walk

Portions of this entry contributed by Margherita Barile

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Cite this as:

Weisstein, Eric W., with contributions by Margherita Barile. "Path." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Path.html

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