Minimum Spanning Trees and Kruskal’s Algorithm (AQA A-Level Further Maths): Flashcards

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Minimum Spanning Trees and Kruskal's Algorithm
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Spanning tree definition

Sub-graph connecting all vertices without cycles

Edges in spanning tree with nn vertices

(n−1)(n-1) edges

Minimum spanning tree (MST) definition

Spanning tree with lowest total weight

Type of algorithm: Kruskal's

Greedy algorithm

Kruskal's algorithm: first step

Select edge with smallest weight

What to check before adding edge in Kruskal's

Check if it creates a cycle

When to stop Kruskal's algorithm

When all vertices are connected

Possible spanning trees for nn vertices

nn−2n^{n-2}

Another name for spanning tree

Connector

Another name for minimum spanning tree

Minimum connector

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