In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is ________.

Answer: 11Concept -- Euler's Formula for Planar Graphs: For any connected planar graph, Euler's formula states: V - E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces (including the unbounded outer face).Given: V = 8, F = 5. Substituting: 8 - E + 5 = 2. Solving: 13 - E = 2, so E = 11.Therefore the graph has 11 edges.

GATE-CS is a competitive examination conducted in India. This question is from the 2021 GATE-CS Discrete Mathematics paper.

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