8 In this question you may use the fact that any simple graph must have an even number of vertices of odd degree.
- A simple graph has five vertices and their degrees are
$$x , x + 1 , x + 1 , x + 2 \text { and } x + 3$$
- Show that \(x\) must be odd.
- Find the value of \(x\) and draw a graph with vertices having the given degrees.
- A simple graph has 10 vertices.
- State the minimum possible degree and maximum possible degree of a vertex.
- Show that the degrees of the vertices cannot all be different.
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