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?

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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`
`text(Vertices = players)`
`text(Edges = games between 2 players)`
`text(S)text(ince each player plays once against the three players)`
`text(in the other team, each vertex must be degree 3.)`
`=> \ B`
A regional airline operates flights in Queensland. Flight times between connected towns are shown in the table.
Draw a network diagram to show how the towns are connected, with weights on the edges showing the flight times. (2 marks)
`text(Edge weights are in minutes duration.)`
Consider the graph below.
Which one of the following is not a path for this graph?
`C`
`text(By trial and error:)`
`text(Consider option)\ C,`
`PTQSR\ text(is not a path because)\ S\ text(to)\ R`
`text(must go through another vertex.)`
`=> C`
In central Queensland, there are four petrol stations `A`, `B`, `C` and `D`. The table shows the length, in kilometres, of roads connecting these petrol stations.
Calculate the shortest distance that can be travelled by the petrol tanker. In your answer, include the order the petrol stations are refilled. (2 marks)
a. 
b. `text(Shortest Path from)\ A\ (text(visiting all stations))`
`A  B  D  C`
`text(Distance)`  `= 170 + 90 + 120` 
`= 380\ text(km)` 
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. (2 marks)
`text(Note the symmetry in this table across the diagonal.)`
The city of Robville is divided into five suburbs labelled as `A` to `E` on the map below.
A lake which is situated in the city is shaded on the map.
A table is constructed to represent the number of land borders between suburbs.
If there is no land border between two suburbs, the table records a '0'. If there is a single land border between two suburbs, the table records a '1', and if there are two separate land borders between the same two suburbs, the table records a '2'.
`{:({:qquadqquadAquadBquadCquadDquadE:}),({:(A),(B),(C),(D),(E):}[(0,1,1,1,0),(1,0,1,2,0),(1,1,0,0,0),(1,2,0,0,0),(0,0,0,0,0)]):}`
In the network diagram below, vertices represent suburbs and edges represent land borders between suburbs.
The diagram has been started but is not finished.
On the diagram
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`
The map of Australia shows the six states, the Northern Territory and the Australian Capital Territory (ACT).
In the network diagram below, each of the vertices `A` to `H` represents one of the states or territories shown on the map of Australia. The edges represent a border shared between two states or between a state and a territory.
i. `text {ACT has 1 border (with NSW)}`
`:.\ text(Degree of ACT's vertex) =1`
ii. `text{NSW is Vertex B (it is connected to the ACT  Vertex D)}`
`:.\ text(Queensland is vertex)\ A\ text(as it is connected)`
`text( to)\ B\ text(and has degree 3.)`
`(C\ text{is Victoria as it has degree 2)}`
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`
`text(Option D has Kwan and Milly as friends which is not correct.)`
`=> D`
Two graphs, labelled Graph 1 and Graph 2, are shown below.
The sum of the degrees of the vertices of Graph 1 is
`C`
`text(Graph 1)`
`∑\ text(degrees)\ = 3 + 3 + 3 + 3 = 12`
`text(Graph 2)`
`∑\ text(degrees)\ = 2 + 2 + 2 + 2 + 2 + 2 = 12`
`=> C`
A store manager is directly in charge of five department managers.
Each department manager is directly in charge of six sales people in their department.
This staffing structure could be represented graphically by
A. a tree.
B. a path.
C. a cycle.
D. a weighted graph.
`A`
`=> A`