6 A connected graph is semi-Eulerian if exactly two of its vertices are of odd degree.
- A graph is drawn with 4 vertices and 7 edges. What is the sum of the degrees of the vertices?
- Draw a simple semi-Eulerian graph with exactly 5 vertices and 5 edges, in which exactly one of the vertices has degree 4 .
- Draw a simple semi-Eulerian graph with exactly 5 vertices that is also a tree.
- A simple graph has 6 vertices. The graph has two vertices of degree 5 . Explain why the graph can have no vertex of degree 1.