1a
2 marks
2 marksA simply connected graph is a connected graph in which any two vertices are directly connected by at most one arc and no vertex is directly connected to itself.
Given that a simply connected graph has exactly four vertices,
(i)
write down the minimum number of arcs it can have,
(ii)
write down the maximum number of arcs it can have.
1b3 marks
3 marks(i)
Draw a simply connected graph that has exactly four vertices and exactly five arcs.
(ii)
State, with justification, whether your graph is Eulerian, semi-Eulerian or neither.
1c5 marks
5 marksBy considering the orders of the vertices, explain why there is only one simply connected graph with exactly four vertices and exactly five arcs.
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