Question-4

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

Answer

\(11\)

Solution

In a connected planar graph, the relationship between the number of vertices (\(n\)), edges (\(e\)), and faces (\(r\)) is given by Euler’s formula:

\(r = e - n + 2\)

Given that \(n = 8\) and \(r = 5\):

\(5 = e - 8 + 2\)

Solving for \(e\):

\(e = 11\)

Therefore, the number of edges in graph G is indeed 11, satisfying Euler’s formula for a connected planar graph.