GATE | GATE-CS-2015 (Set 1) | Question 65
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is _______________.
Explanation: Euler’s formula states that if a finite, connected, planar graph is drawn in the plane without any edge intersections, then
v − e + f = 2. v -> Number of vertices e -> Number of edges f -> Number of faces As per the question v = 10 And number of edges on each face is three Therefore, 2e = 3f [Note that every edge is shared by 2 faces] Putting above values in v − e + f = 2 10 - e + 2e/3 = 2 e = 3*10 - 6 = 24
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