1 of 8 0-day streak

A full network investigation

Question 1 of 8

Calculator allowed

Consider this plan of walking tracks between park locations. The graph is connected and can be drawn in planar form. Each edge label gives the walking distance in kilometres

(a)3 marks

Record v and e for this graph and calculate f using v + f = e + 2

v e f

(b)1 mark

Determine the number of odd-degree vertices in the network

Number of odd vertices

Decide whether an edge-exact closed traversal exists. Choose the matching 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

What is the minimum route total between Gate and Picnic Area?

Shortest-path total (km)

(e)1 mark

What is the least possible total walking distance for walking-track sections reaching all vertices?

Minimum connector total (km)