# Definition:Cycle (Graph Theory)

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## Contents

## 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

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 2.3$: Connected Graphs