Question 6 - A-Level Maths

The complete graph \(K _ { n }\) has every one of its \(n\) vertices connected to each of the other vertices by a single edge.
1. Find the total number of edges in the graph \(K _ { 5 }\).
2. State the number of edges in a minimum spanning tree for the graph \(K _ { 5 }\).
3. State the number of edges in a Hamiltonian cycle for the graph \(K _ { 5 }\).
A simple graph \(G\) has six vertices and nine edges, and \(G\) is Eulerian. Draw a sketch to show a possible graph \(G\).
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