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?
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`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`
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.
--- 1 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
i. `1`
ii. `text{NSW is Vertex B (it is connected to the ACT – Vertex D)}`
`=> C\ text{is Victoria as it has degree 2}`
`:.\ text(Queensland is vertex)\ A\ text(as it is connected to)\ B\ text(and has degree 3.)`
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)}`
`=> C\ text{is Victoria as it has degree 2}`
`:.\ text(Queensland is vertex)\ A\ text(as it is connected to)\ B\ text(and has degree 3.)`
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`