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Math Help - Wheel graph and complete graph

  1. #1
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    Wheel graph and complete graph

    Hello, since the wheel graph with 3 vertices on the rim and 1 vertex in the middle is the same as the complete graph on 4 vertices, should I not be able to derive the general wheel graph chromatic polynomial for W3 from the general chromatic polynomial for a Complete graph(4)? .

    I would write it up here, but it's pointless because all i am doing is expanding the elements inside of the brackets, but this is clearly not going to reach the general chromatic polynomial for a wheel graph.

    Wheel graph Chromatic polynomial with 3 vertices on the rim is x(x-2)^3 +(-1)^3(x-2)

    Complete graph on 4 vertices is x(x-1)(x-2)(x-3).

    so should is not be the case that x(x-1)(x-2)(x-3)==x((x-2)^3 +(-1)^3(x-2)) ?


    Edit: OK, i substituted x with a random number and then computed each polynomial and have gotten the same result from both polynomials with the same value for x, so they are clearly the same. I just need to show it algebraically.

    Edit: OK, that was easy. I was clearly over thinking it. If i knew how to delete the thread i would.

    Thanks.
    Last edited by takaj; September 29th 2012 at 07:42 PM.
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