Year 12 Mathematics Applications
Graph and Networks
1. A technology company is having cable installed to connect workstations.
The network below represents the cost of cabling each section.
Calculate the total cost of the installation.
2.
The diagram below shows the distances between towns on a map in kilometres (not to scale). List
the possible paths between Alphaville, at point A and Epsilon Town at point E.
Find the shortest path that can be travelled between the two towns. You must always travel in the
direction away from Alphaville towards Epsilon Town.
Year 12 Mathematics Applications
Graph and Networks
Look carefully at each of the networks below. Complete the questions which follow.
3.
a.
c.
b.
e.
i.
f.
g.
h.
j.
k.
l.
List which of the above networks satisfy each of the following:
a. Is a simple graph:
b. Has multiple edges:
c. Contains a loop:
d. Is a digraph:
e. Is a digraph with multiple edges:
f.
d.
Is a digraph with a loop:
g. Is a complete graph:
Year 12 Mathematics Applications
4.
5.
Graph and Networks
In the space provided, sketch the complete graph 𝐾𝐾6 .
𝐾𝐾8 is the complete graph with 8 vertices. Without drawing the graph of 𝐾𝐾8 find how many
edges it has.