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Tickets order confirmed I Asos saved Tabs Apple icloud 61005 Yahoo Bing Facebook Twitter Linkedin The Weather Channel cuny STUDENTs s 175 M243ea D47553) combinatorial Geometry Taive Testa Euler's theorem on planar graphs Save and submi A Click Submit to complete this assessment. Question 2 10 points save An Given a connected planar graph G with v 8 vertices. Let EandFbe the number of edges and faces. Assume thatGis face-regular, i e, every face has the same egree number of edges along the border of the face.) Find the number of faces for face-degree 2, 34, 5, and 6. Bface-degree- 3 a, F-8 face-degree 4 b F-4 c. Fa 10 face-degree -5 face-degree 6 d.Fa 3 face-degree 2 e.Fa 12 F-6 g No such graph i, F 16 F-2, 3, 4. 14 S

Explanation / Answer

(Euler's Formula)  

Let G be a connected planar graph, and let V, E and F denote, respectively, the numbers of vertices, edges, and faces in a plane drawing of G. Then V - E + F = 2.

so,

1)8-3*2+x=2

x=0;

No such graph

2)

8-4*2+x=2

x=2

3)

8-5*2+x=2

x=4

4)

8-6*2+x=2

x=6

g) 8-2*2+x=2

x=-2

No such graphs

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