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.Show that for any planar graph, V-e+f = 2 ニ

.Show that for any planar graph, V-e+f = 2 ニ

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.5: The Format Proof Of A Theorem
Problem 12E: Based upon the hypothesis of a theorem, do the drawings of different students have to be identical...
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A. Answer the following question accordingly. It shouldn’t take that long. Thanks in advance!
1. Show that for any planar graph, V-e+f = 2 In the example above, we have V=6,e =7,f= 3 which is 6-7t3=2 Hint: consider inducting the number of edges. what does adding an edge do to the number of faces?
Transcribed Image Text:1. Show that for any planar graph, V-e+f = 2 In the example above, we have V=6,e =7,f= 3 which is 6-7t3=2 Hint: consider inducting the number of edges. what does adding an edge do to the number of faces?
The following is a planar graph that can be drawn in the plane without any edge crossings. We can evaluate not only the edges and vertices with the given graph but also the faces (areas that are enclosed by edges) 3 Remember: If there are no areas enclosed by edges, as in a tree, we say there is 1 face
Transcribed Image Text:The following is a planar graph that can be drawn in the plane without any edge crossings. We can evaluate not only the edges and vertices with the given graph but also the faces (areas that are enclosed by edges) 3 Remember: If there are no areas enclosed by edges, as in a tree, we say there is 1 face
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