AQA D1 2016 June — Question 6

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2016
SessionJune
TopicGraph Theory Fundamentals

6 A connected graph is semi-Eulerian if exactly two of its vertices are of odd degree.
  1. A graph is drawn with 4 vertices and 7 edges. What is the sum of the degrees of the vertices?
  2. Draw a simple semi-Eulerian graph with exactly 5 vertices and 5 edges, in which exactly one of the vertices has degree 4 .
  3. Draw a simple semi-Eulerian graph with exactly 5 vertices that is also a tree.
  4. 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.