Question 1.49

19.

  1. Can you draw a graph that is connected and for which the valences of vertices are the consecutive integers from 2 to 6?
  2. If a graph such as the one described in part (a) exists, can it have an Euler circuit? (Explain your answer.)

19.

(a)

image

(b) No. To have an Euler circuit a graph cannot have odd-valent vertices.