### Minimal spanning trees

This post will contain the following information about minimal spanning trees in HSC Standard Math.

- What are ‘trees’
- What are spanning trees
- What are minimum spanning trees
- Using Prim’s and Kruskal’s algorithms to find minimal spanning trees

### What are ‘trees’?

A **tree** is a connected graph that contains no cycles, multiple edges or loops. The following videos explain what trees are and provide examples on how to solve questions.

Example:

### What are spanning trees

A **spanning tree** is a tree that connects all of the vertices of a graph. The following videos explain what spanning trees are and provide examples on how to solve questions.

Example:

### What is a minimum spanning tree

A **minimum spanning tree** is a spanning tree with a minimum length. It connects all the vertices together with the minimum total weighting for the edges.

### Using Prim’s and/or Kruskal’s algorithms to determine minimum spanning trees

##### Prim’s Algorithm

##### Kruskal’s Algorithm