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.

Also known as

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

A minimum spanning tree can also be called the minimum connector for $G$.

Also see

• Minimum Spanning Tree is not necessarily Unique

• Definition:Maximum Spanning Tree

Sources

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