In the complete graph \(\mathrm { K } _ { 7 }\), every one of the 7 vertices is connected to each of the other 6 vertices by a single edge.
Find or write down:
the number of edges in the graph;
the number of edges in a minimum spanning tree;
the number of edges in a Hamiltonian cycle.
Explain why the graph \(\mathrm { K } _ { 7 }\) is Eulerian.
Write down the condition for \(\mathrm { K } _ { n }\) to be Eulerian.
A connected graph has 6 vertices and 10 edges.
Draw an example of such a graph which is Eulerian.