In an undirected connected planar graph G, there are eight vertices and five…
2021
In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is _________.
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Correct answer: 11
Key idea: Use Euler's formula for connected planar graphs: V - E + F = 2.
Substitute the given values V = 8 and F = 5 into the formula: 8 - E + 5 = 2.
Solve for E: 13 - E = 2, so E = 11.
Answer: 11 edges.