# Definition:Minimum Spanning Tree

## Definition

Let $G$ be a weighted graph.

The **minimum spanning tree** for $G$ is a spanning tree for $G$ which has a minimum total weight.

For a given $G$, the minimum spanning tree may not be unique.

It can also be called the **minimum connector** for $G$.

## Also known as

A **minimum spanning tree** is also known as an **economy tree**.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 4.1$: The Minimal Connector Problem: An Introduction to Trees