Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » discretemath

Topic: a question involving Eular's formula
Replies: 1   Last Post: Oct 23, 2012 7:45 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Mike Katherein

Posts: 1
From: N/A
Registered: 10/23/12
a question involving Eular's formula
Posted: Oct 23, 2012 6:17 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.