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Finding the eigenvalue for a given graph

  1. Dec 8, 2004 #1
    I'm having trouble finding the eigenvalue for a given graph; but more specifically I can't seem to find the characteristic polynomial. My book tells me that the characteristic polynomial of a simple graph with n vertices is the determinant of the matrix (A-[tex]\lambda[/tex]I), where A is the adjaceny matrix and I is the n X n identity matrix. What is [tex]\lambda[/tex]? And I've read someplace else that the characteristic equation of a matrix is the determinant of (xI-A) - which is right, or are they both?
    And isn't the root of the equation the eigenvalue?
  2. jcsd
  3. Dec 8, 2004 #2

    matt grime

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    lambda is a variable, use x if you prefer. It's just a letter.
  4. Dec 8, 2004 #3
    Ah yes of course, I had thought as much. Thank you very much. (It works now!)
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