3. (b) The degree of every vertex of a graph G is one of three consecutive integers. If, for each of the three consecutive integers x, the graph G contains exactly x vertices of degree x, prove that...

3. (b) The degree of every vertex of a graph G is one of three consecutive integers. If, for each of the three consecutive integers x, the graph G contains exactly x vertices of degree x, prove that two-thirds of the vertices of G have odd degree.

(c) Construct a simple graph with 12 vertices satisfying the property described in part (b).