Definition:Cycle (Graph Theory)

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Definition

A cycle is a circuit in which no vertex except the first (which is also the last) appears more than once.

Alternatively, a cycle can be defined as a closed path.


An $n$-cycle is a cycle with $n$ vertices.


The set of vertices and edges which go to make up a cycle form a subgraph.

This subgraph itself is also referred to as a cycle.


Odd Cycle

An odd cycle is a cycle with odd length, that is, with an odd number of edges.


Even Cycle

An even cycle is a cycle with even length, that is, with an even number of edges.


Sources