# Girth of a graph

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Template:Undirected graph numerical invariant

## Definition

Suppose is an undirected graph. The **girth** of is defined as the minimum possible length of a cycle of length 3 or more (i.e., a subgraph isomorphic to a cycle graph) in .

## Related invariants

- Even girth refers to the minimum among the lengths of all cycles of even length.
- Odd girth refers to the minimum among the lengths of all cycles of odd length.

The girth of a graph is the minimum of its even girth and odd girth.

## Related graph properties

- Forest and tree: Note that the girth of a graph is if and only if the graph is a forest. For a connected graph, the girth is if and only if the graph is a tree.
- Triangle-free graph is a graph of girth 4 or more