For the following planar graphs, determine the number of vertices v, edges e, and faces f: i. v=9,e=16,f=9; ii. v=7,e=14,f=9. Verify Euler's formula v−e+f=2.
A number or a short expression. Spacing and $ signs are ignored.
Solution
i. For the graph with v=9,e=16,f=9, Euler's formula v−e+f=2 holds as 9−16+9=2. ii. For the graph with v=7,e=14,f=9, Euler's formula v−e+f=2 holds as 7−14+9=2.
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