Basic Concepts
Drawing a Network
100
The graph below represents a friendship network. The vertices represent the four people in the friendship network: Kwan (K), Louise (L), Milly (M) and Narelle (N).
An edge represents the presence of a friendship between a pair of these people. For example, the edge connecting K and L shows that Kwan and Louise are friends.
Which one of the following graphs does not contain the same information?
D
200
Consider the graph below.
Which one of the following is not a path for this graph?
A. PRQTS
B. PRTSQ
C. PTQSR
D. PTRQS
C
300
Consider the network diagram.
What is the sum of the degrees of all the vertices in this network?
16
300
A network of roads between towns shows the travelling times in minutes between towns that are directly connected.
Complete the shaded cells in the following table so that it represents the information in this network.
400
Team A and Team B have entered a chess competition.
Team A and B have three members each. Each member of Team A must play each member of Team B once.
Which of the following network diagrams could represent the chess games to be played?
B
400
The table below represents a directed network.
Create a network diagram to accurately reflect the network described in the above table.
Answers will vary
500
An undirected connected graph has five vertices.
Three of these vertices are of even degree and two of these vertices are of odd degree.
One extra edge is added. It joins two of the existing vertices.
In the resulting graph, it is not possible to have five vertices that are
A. all of even degree.
B. all of equal degree.
C. one of even degree and four of odd degree.
D. four of even degree and one of odd degree.
D
500
A directed network diagram is pictured below.
The information in the network diagram is used to complete the network table below, with a "0" used to signify that no connection exists. Complete the table. (2 marks)
