Results 1 to 2 of 2

Math Help - Graph Theory.

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    12

    Graph Theory.

    If a graph has 16 vertices, 35 edges and degree set {4, 5}. How many vertices of degree 4 are there?


    Please help, it's much appreciated.
    Last edited by mr fantastic; May 15th 2010 at 10:53 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2010
    From
    Bratislava
    Posts
    115
    Quote Originally Posted by MathHelp12345 View Post
    If a graph has 16 vertices, 35 edges and degree set {4, 5}. How many vertices of degree 4 are there?


    Please help, it's much appreciated.
    Let v1 be the number of vertices of degree 4 and v2 be the number of vertices of degree 5.
    We know that v1+v2=16 and from handshake lemma we get that 4v1+5v2=70.

    So you only need to solve the system of 2 linear equations
    v1+v2=16
    4v1+5v2=70

    Solution is v1=10, v2=6.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Graph theory, bipartite Graph
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: March 10th 2012, 05:47 AM
  2. Graph Theory / Chromatic Number of a Complete Graph
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 15th 2011, 09:59 AM
  3. (Graph Theory)Prove that graph X is a tree.
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: August 1st 2011, 03:30 AM
  4. Replies: 0
    Last Post: September 25th 2010, 05:59 AM
  5. Graph Theory - Size of a Line Graph
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: July 25th 2010, 11:15 PM

Search Tags


/mathhelpforum @mathhelpforum