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Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is
- a)6
- b)8
- c)9
- d)13
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let G be a simple connected planar graph with 13 vertices and 19 edges...
An undirected graph is called a planar graph if it can be drawn on a paper without having two edges cross and such a drawing is called Planar Embedding. We say that a graph can be embedded in the plane, if it planar. A planar graph divides the plane into regions (bounded by the edges), called faces. Graph K4 is palanar graph, because it has a planar embedding as shown in figure below.
Euler's Formula : For any polyhedron that doesn't intersect itself (Connected Planar Graph),the • Number of Faces(F) • plus the Number of Vertices (corner points) (V) • minus the Number of Edges(E) , always equals 2. This can be written: F + V − E = 2. Solution : Here as given, F=?,V=13 and E=19 -> F+13-19=2 -> F=8 So Answer is (B).
Most Upvoted Answer
Let G be a simple connected planar graph with 13 vertices and 19 edges...
To find the number of faces in the planar embedding of a graph, we can use Euler's formula, which states that for any simple connected planar graph, the number of vertices (V), edges (E), and faces (F) are related by the equation V - E + F = 2.
Given that the graph G has 13 vertices and 19 edges, we can substitute these values into Euler's formula to find the number of faces.
V = 13 (number of vertices)
E = 19 (number of edges)
F = ?
V - E + F = 2
13 - 19 + F = 2
F - 6 = 2
F = 8
Therefore, the number of faces in the planar embedding of the graph is 8 (option B).
Explanation:
- Euler's formula relates the number of vertices, edges, and faces of a simple connected planar graph.
- We are given that the graph G has 13 vertices and 19 edges.
- By substituting these values into Euler's formula, we can solve for the number of faces.
- Simplifying the equation, we find that F = 8, indicating that there are 8 faces in the planar embedding of the graph.
- Therefore, the correct answer is option B.
Given that the graph G has 13 vertices and 19 edges, we can substitute these values into Euler's formula to find the number of faces.
V = 13 (number of vertices)
E = 19 (number of edges)
F = ?
V - E + F = 2
13 - 19 + F = 2
F - 6 = 2
F = 8
Therefore, the number of faces in the planar embedding of the graph is 8 (option B).
Explanation:
- Euler's formula relates the number of vertices, edges, and faces of a simple connected planar graph.
- We are given that the graph G has 13 vertices and 19 edges.
- By substituting these values into Euler's formula, we can solve for the number of faces.
- Simplifying the equation, we find that F = 8, indicating that there are 8 faces in the planar embedding of the graph.
- Therefore, the correct answer is option B.
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Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph isa)6b)8c)9d)13Correct answer is option 'B'. Can you explain this answer?
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