Question 1.37

7. In the accompanying graph, the vertices represent houses and two vertices are joined by an edge if it is possible to drive between the two houses in under 10 minutes.

image
  1. How many vertices does the graph have?
  2. How many edges does the graph have?
  3. What are the valences of the vertices in this graph?
  4. Based on the information given by the graph, for which houses, if any, is it possible to drive to all the other houses in less than 20 minutes?
  5. Based on the graph, from house B which houses require a trip of longer than 20 minutes?

7.

(a) Eight vertices

(b) 13 edges

(c) A: 4; B: 2; C: 3; D: 3; E: 4; F: 4; G: 3; H: 3

(d) A, D, and F

(e) E, G, and H