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## Summary/Background

A tree is a connected graph with no cycles. A spanning tree is a subgraph which includes all the vertices of a graph and is also a tree. A minimum spanning tree (or minimum connector) is a spanning tree such that the total length of its edges is as small as possible.
Note: The number of edges in the minimum spanning tree is one less than the number of vertices.

Java applet from Algorithms

## Glossary

### connected

of two vertices if there is a path between them.

### graph

A diagram showing a relationship between two variables.
The diagram shows a vertical y axis and a horizontal x axis.

### minimum spanning tree

A spanning tree such that the total length of its edges is as small as possible.

### spanning tree

A subgraph which includes all the vertices of a graph and is also a tree.

### tree

A connected graph with no cycles.

Full Glossary List

## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)D1Algorithms on graphsMinimum connector-
AQA AS Further Maths 2017Discrete MathsNetworksMinimum Connector-
AQA AS/A2 Further Maths 2017Discrete MathsNetworksMinimum Connector-
Edexcel A-Level (UK - Pre-2017)D1Algorithms on graphsMinimum connector-
Edexcel AS Further Maths 2017Decision Maths 1Algorithms on GraphsMinimum Connector-
Edexcel AS/A2 Further Maths 2017Decision Maths 1Algorithms on GraphsMinimum Connector-
I.B. Higher Level10Algorithms on graphsMinimum connector-
OCR A-Level (UK - Pre-2017)D1Algorithms on graphsMinimum connector-
OCR AS Further Maths 2017Discrete MathsNetwork AlgorithmsMinimum Connector-
OCR MEI AS Further Maths 2017Modelling with AlgorithmsNetworksMinimum Connector-
OCR-MEI A-Level (UK - Pre-2017)D1Algorithms on graphsMinimum connector-
Universal (all site questions)AAlgorithms on graphsMinimum connector-