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
The Answer to the Question
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Here's the Solution to this Question
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: