Question 4 (a) For each of the following graphs, give all perfect matchings of the graph. 1 2 3 1 5 4 1 сл 2 LO 3 6

Which of the following graphs exhibit ALL of the listed properties

Which of the following graphs have Euler circults or Euler tralts? O B: Has Euler trail. OB: Has Euler circuit. OA: Has Euler trail. OA: Has Euler circuit. OC: Has Euler trail. OC: Has Euler circuit. OD: Has Euler trail. OD: Has Euler circuit.

9.1 Explain whether a graph with each of the following characteristics exists. If so, give an example. If not, justify your answer. (a) A planar graph with 6 vertices, 10 edges and 5 faces. (b) A planar graph G with 6 vertices with degrees 2, 2, 3, 4, 4, 5. (c) A planar graph with 7 vertices, 10 edges and 4 faces. (d) A planar graph with 10 vertices and edges.