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
The number of edges is equal to half the sum of the degrees of the vertices. Then
By Euler's formula, . Then the number of graph faces is
Let's draw a planar graph: