3. (a) Is it possible to have a 4-regular graph with 15 vertices? If no, explain why. If yes, construct such a graph. (b) The degree of every vertex of a graph G is one of three consecutive integers....

Extracted text: 3. (a) Is it possible to have a 4-regular graph with 15 vertices? If no, explain why. If yes, construct such a graph. (b) The degree of every vertex of a graph G is one of three consecutive integers. If, for each of the three consecutive integers r, the graph G contains exactly r vertices of degree r, prove that two-thirds of the vertices of G have odd degree.