Question 1.45

15. Draw a graph with eight vertices that is connected where each vertex has

  1. degree (valence) 2.
  2. valence 3.
  3. valence 4.
  4. Do all graphs with eight vertices having valence 2 have the same number of edges?

15.

Drawings can vary. Possible renderings for parts (a) through (c) include the following:

(a)

image

(b)

image

(c)

image

(d) Yes