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VCE 11 General 2023

8.01 Introduction to graphs

Worksheet
Edges and vertices
1

State the number of vertices and edges for each of the following networks:

a
b
2

Determine if the following networks are valid:

a
b
c
d
e
f
g
h
3

Consider the following network:

a

Are there more vertices or more edges?

b

Is this property true for all networks?

4

For the following network, list the pairs of vertices that are connected by an edge.

5

Determine whether the following statements are true or false in regard to networks:

a

There is always at least one vertex.

b

There is always at least one edge.

c

All vertices must be connected to every other vertex by edges.

d

An edge can start and end at the same vertex.

e

Edges always start and end at vertices.

f

An edge can connect three vertices together.

6

For each of the given networks:

i

State the number of vertices.

ii

State the number of edges.

iii

Find the degree of each vertex.

iv

Is the network connected?

a
b
Directed networks
7

State whether the following are directed or undirected networks:

a
b
c
d
e
f
g
h
i
j
k
l
8

In the following directed network, there is an edge from A to B. List the remaining edges.

9

State whether the following are best represented by an undirected or directed network:

a

Which countries border each other

b

The results of an elimination-style sports tournament

c

The animals that different animals eat

d

Your parents and their ancestors

e

Ways to get from one classroom to another at school

f

How parts of the body are connected

Simple networks
10

How many loops are in the following networks:

a
b
c
d
11

State whether the following networks contain a pair of vertices that have multiple edges between them:

a
b
c
d
12

State whether the following networks are simple:

a
b
c
d
e
f
13

State the two changes required to make the following network simple:

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Outcomes

U2.AoS2.1

the language, properties and types of graphs, including edge, face, loop, vertex, the degree of a vertex, isomorphic and connected graphs, and the adjacency matrix, Euler’s formula for planar graphs, and walks, trails, paths, circuits, bridges and cycles in the context of traversing a graph

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