Date: Oct 23, 2012 6:17 PM
Author: Mike Katherein
Subject: a question involving Eular's formula

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.)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I am a super-newbie 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