Results 1 to 3 of 3

Math Help - Vertices help

  1. #1
    Super Member
    Joined
    Oct 2007
    From
    Santiago
    Posts
    517

    Vertices help

    Hey guys need help with this question. "A graph has 33 edges, and every vertex has degree 7 or degree 8. How many vertices does the graph have?".

    Any help would be much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,970
    Thanks
    1011
    From the handshaking lemma

    \sum{\textrm{deg}\,(v)} = 2|E|


    Since there are 33 edges, that means \sum{\textrm{deg}\,(v)} = 66.


    That means that 7m + 8n = 66, where m is the number of vertices with degree 7 and n is the number of vertices with degree 8.


    By inspection, m = 6 and n = 3.

    So there are 9 vertices.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Oct 2007
    From
    Santiago
    Posts
    517
    Quote Originally Posted by Prove It View Post
    From the handshaking lemma

    \sum{\textrm{deg}\,(v)} = 2|E|


    Since there are 33 edges, that means \sum{\textrm{deg}\,(v)} = 66.


    That means that 7m + 8n = 66, where m is the number of vertices with degree 7 and n is the number of vertices with degree 8.


    By inspection, m = 6 and n = 3.

    So there are 9 vertices.
    Thank you for your reply! Nice and clear.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vertices
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 19th 2009, 10:05 AM
  2. coordinates and vertices help~*~
    Posted in the Geometry Forum
    Replies: 0
    Last Post: May 25th 2009, 07:36 PM
  3. Vertices in polyhedron
    Posted in the Geometry Forum
    Replies: 0
    Last Post: February 17th 2009, 03:09 AM
  4. vertices??? and transformation...
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 11th 2008, 07:29 PM
  5. Vertices help
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: August 19th 2007, 09:28 PM

Search Tags


/mathhelpforum @mathhelpforum