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7.01 Trees and spanning trees

Interactive practice questions

Consider the following graphs.

a

Which of these graphs is a tree?

A

B

C

A

B

C
b

Why is the following graph not a tree?

It is disconnected.

A

It has a loop.

B

It has multiple edges connecting the same vertices.

C

it has a circuit.

D

It is disconnected.

A

It has a loop.

B

It has multiple edges connecting the same vertices.

C

it has a circuit.

D
c

Why is the following graph not a tree?

It has a loop.

A

It is disconnected.

B

It has a circuit.

C

It has multiple edges connecting the same vertices.

D

It has a loop.

A

It is disconnected.

B

It has a circuit.

C

It has multiple edges connecting the same vertices.

D
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Consider the following graphs.

Given the following networks:

In graph theory terms, what is a tree?

Outcomes

ACMGM101

explain the meaning of the terms tree and spanning tree identify practical examples

ACMGM102

identify a minimum spanning tree in a weighted connected graph either by inspection or by using Prim’s algorithm

ACMGM103

use minimal spanning trees to solve minimal connector problems; for example, minimising the length of cable needed to provide power from a single power station to substations in several towns

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