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Networks, STD1 N1 2020 HSC 9 MC

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`

Show Worked Solution

`text(Vertices = players)`

♦♦ Mean mark 34%.

`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`

Filed Under: Uncategorized Tagged With: Band 5, smc-1136-50-Other

Networks, STD2 N2 SM-Bank 37

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. In the network diagram, what is the order of the vertex that represents the Australian Capital Territory (ACT)?  (1 mark)

    --- 1 WORK AREA LINES (style=lined) ---

  2. In the network diagram, Queensland is represented by which letter? Explain why.  (2 marks)

    --- 4 WORK AREA LINES (style=lined) ---

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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.)`

Show Worked Solution

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.)`

Filed Under: Basic Concepts, Basic Concepts, Basic Concepts, Network Concepts (Std2-2027) Tagged With: Band 4, num-title-ct-extension, smc-1136-40-Degrees of Vertices, smc-1136-50-Other, smc-4788-60-Connected graphs, smc-4788-70-Applications, smc-6307-30-Map to Network, smc-6307-50-Degree of Vertices, smc-912-25-Map to Network, smc-912-40-Degrees of Vertices

Networks, STD2 N2 2015 FUR1 5 MC

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.
 
 

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`D`

Show Worked Solution

`text(Option D has Kwan and Milly as friends which is not correct.)`

`=> D`

Filed Under: Basic Concepts, Basic Concepts, Basic Concepts, Network Concepts (Std2-2027) Tagged With: Band 2, num-title-ct-path, smc-1136-50-Other, smc-4788-40-Planar graphs, smc-6307-60-Other, smc-912-50-Other

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