Trees and Minimum Connector Problems (VCE SSCE General Mathematics): Quizzes

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Trees and Minimum Connector Problems
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What is a tree in graph theory?

A graph with no loops, multiple edges, or cycles

If a tree has nn vertices, how many edges does it have?

n1n - 1 edges

What is a spanning tree?

A tree that connects all vertices of a graph

A graph has 99 vertices and 1313 edges. How many edges must be removed for a spanning tree?

55 edges

What is the minimum spanning tree?

The spanning tree with smallest total weight

What is the first step in Prim's algorithm?

Choose any vertex as starting point

In Prim's algorithm, what must you avoid when selecting edges?

Edges that create a cycle

How do connector problems differ from shortest path problems?

They find min total to connect all points

A spanning tree has edges with weights 2,5,3,5,22, 5, 3, 5, 2. What is the total weight?

1717

What is a common application of minimum spanning trees?

Connecting towns to utilities efficiently

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