Question

6 b) If a planar graph has the degree sequence (2,2,2,3,4,4,5), how many faces will it

have? Draw a planar graph with this degree sequence and the number of faces

obtained to check your answer

Answer 1

By condition, the number of vertices in the graph is

$V = 7$

The number of edges is equal to half the sum of the degrees of the vertices. Then

$E = \frac{{2 + 2 + 2 + 3 + 4 + 4 + 5}}{2} = 11$

By Euler's formula, $V - E + F = 2$ . Then the number of graph faces is

$F = 2 - V + E = 2 - 7 + 11 = 6$

Let's draw a planar graph: