Solution to If a planar graph has the degree sequence (2,2,2,3,4,4,5), how many faces will it have? … - Sikademy
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Archangel Macsika

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

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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:


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