QCAA General Mathematics Graphs and networks

A bridge is a specific type of edge whose removal increases the number of connected components in a graph, not a type of walk.

A loop is an edge that connects a vertex to itself, rather than a sequence of vertices and edges known as a walk.

A path is a walk where all vertices must be distinct. Since the question specifies that vertices are repeated, it cannot be a path.

A trail is defined as a walk in which no edges are repeated, but vertices are allowed to be repeated.

Incorrect. This incorrectly adds the number of vertices and edges ($3 + 5 = 8$) instead of applying Euler's formula.

Incorrect. This is a miscalculation; applying Euler's formula ($V - E + F = 2$) with $V=3$ and $E=5$ does not result in 6 faces.

Correct. By Euler's formula for planar graphs ($V - E + F = 2$), substituting $V = 3$ and $E = 5$ gives $3 - 5 + F = 2$, which means there are $F = 4$ faces.

Incorrect. This is the constant value in Euler's formula ($V - E + F = 2$), not the calculated number of faces.

This number corresponds to the number of vertices (teams) in the graph, not the number of edges (games played).

The table contains 18 checkmarks total. Since each game involves two teams and is recorded for both, the number of edges is half the total count: $18 \div 2 = 9$.

This would be the number of edges if every team played every other team (a complete graph $K_6$), calculated as $\frac{6 \times 5}{2} = 15$.

This is the total number of checkmarks in the table. Because the graph is undirected (Team A vs Team B is the same game as Team B vs Team A), you must divide this sum by 2.