A cycle in a graph, digraphMathworldPlanetmath, or multigraphMathworldPlanetmath, is a simple path from a vertex to itself (i.e., a path where the first vertex is the same as the last vertex and no edge is repeated).

For example, consider this graph:


ABCDA and BDAB are two of the cycles in this graph. ABA is not a cycle, however, since it uses the edge connecting A and B twice. ABCD is not a cycle because it begins on A but ends on D.

A cycle of length n is sometimes denoted Cn and may be referred to as a polygonMathworldPlanetmathPlanetmath of n sides: that is, C3 is a triangle, C4 is a quadrilateralMathworldPlanetmath, C5 is a pentagonMathworldPlanetmath, etc.

An even cycle is one of even length; similarly, an odd cycle is one of odd length.

Title cycle
Canonical name Cycle
Date of creation 2013-03-22 12:17:21
Last modified on 2013-03-22 12:17:21
Owner mps (409)
Last modified by mps (409)
Numerical id 8
Author mps (409)
Entry type Definition
Classification msc 05C38
Related topic AcyclicGraph
Related topic SimplePath
Related topic VeblensTheorem
Related topic MantelsTheorem
Related topic Graph