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a question involving Eular's formula
Posted:
Oct 23, 2012 6:17 PM


G is a planar graph that has n vertices, e edges, r regions, and k connected components.
Show that the Euler's Formula for G can be written as: n  e + r = k + 1. (Remember if G is connected, then k = 1, which means Euler's Formula will be degenerated to n  e + r = 2.)
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I am a supernewbie to discrete math, and I don't even know where I should start with this question
I only know that the Eular's theorem for any connected planar graph is n  e + r = 2.
But I don't know how could I transform that formula to n  e + r = k + 1.
any hints or helps will be appreciated, thanks for reading this post



