1 of 8 0-day streak

A full network investigation

Question 1 of 8

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A proposed network of roads between coastal towns is shown below. The graph is connected and can be drawn in planar form. Each edge label gives the road distance in kilometres

(a)3 marks

Count the vertices and edges, then use Euler's formula to find the number of faces

v e f

(b)1 mark

How many vertices have odd degree?

Number of odd vertices

Can every connection be traversed exactly once while returning to the starting vertex? Select the correct verdict and reason

Yes. The graph is connected and every vertex has even degree

No. The graph is connected with exactly two odd vertices, so only an open Eulerian trail is possible

No. Four odd vertices prevent an Eulerian trail or circuit

No. The edge set is split into disconnected components

(d)1 mark

Find the shortest total road distance from Anglesea to Torquay

Shortest-path total (km)

(e)1 mark

Find the minimum total road distance for a set of roads that reaches every vertex

Minimum connector total (km)