1. Graphs Definition: a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges.

3. A vertex is a point where edges meet An edge can start and end at the same vertex

4. A vertex is a point where edges meet An edge can start and end at the same vertex

5. A vertex is a point where edges meet Vertices are also known as nodes Edges are also known as arcs

6. A weight is a number associated with an edge

7. This could represent a distance, time or cost

8. A path runs from one vertex to another along edges but no vertex is passed through more than once

9. A path runs from one vertex to another along edges but no vertex is passed through more than once

10. A closed path returns to the start

11. This is also known as a circuit or cycle

12. In a connected graph it is possible to find a path between any two vertices:

13. This graph is not connected:

14. A tree is a connected graph of some vertices which contains no cycles

16. A spanning tree is a connected graph of all vertices which contains no cycles

17. The minimum spanning tree is the spanning tree with the least weight Length of this tree is 19

18. The minimum spanning tree is the spanning tree with the least weight Can you find the least weight?

19. The minimum spanning tree is the spanning tree with the least weight The least weight is 15

20. The minimum spanning tree is the spanning tree with the least weight The least weight is 15