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Networks, GEN1 2023 VCAA 34 MC

A bipartite graph is typically used to display which one of the following?

  1. the allocation of tasks on a construction site
  2. the path used to visit five different construction sites
  3. the total distance travelled between two construction sites
  4. the critical path of activities to be completed in a construction project
  5. the minimum length of cable required to connect six construction sites
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\(A\)

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Consider option A:

Individuals or groups can be represented by a column of nodes and tasks can be represented by a second column, allowing for edges to indicate the allocation of tasks.

\(\Rightarrow A\)

NETWORKS, FUR1 2016 VCAA 3 MC

The following graph with five vertices is a complete graph.
 

Edges are removed so that the graph will have the minimum number of edges to remain connected.

The number of edges that are removed is

  1.   `4`
  2.   `5`
  3.   `6`
  4.   `9`
  5. `10`
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`C`

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`text(The minimum number of edges for)`

♦♦ Mean mark 35%.

`text{a connected graph is 4 (spanning tree).}`
 

 
`:.\ text(Edges to be removed)`

`= 10 – 4`

`= 6`

`=> C`

NETWORKS, FUR1 2006 VCAA 7 MC

A complete graph with six vertices is drawn.

This network would best represent

  1. the journey of a paper boy who delivers to six homes covering the minimum distance.
  2. the cables required to connect six houses to pay television that minimises the length of cables needed.
  3. a six-team basketball competition where all teams play each other once.
  4. a project where six tasks must be performed between the start and finish.
  5. the allocation of different assignments to a group of six students.  
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`C`

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`text(A complete graph has all vertices connected)`

`text(directly to all other vertices without any)`

`text(parallel edges or loops.)`

`rArr C`

NETWORKS, FUR1 2013 VCAA 2 MC

The number of edges needed to make a complete graph with four vertices is

A.   `2`

B.   `3`

C.   `4`

D.   `5`

E.   `6`

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`E`

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`text(Let)\ \ v=\ text(number of vertices)`

`text(Number of Edges)` `= (v(v – 1))/2`
  `= (4 xx 3)/2`
  `= 6`

 
`=>  E`