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Thread: Adjacency Matrix

  1. September 1st 2010, 01:32 AM #1
    raed
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    Adjacency Matrix

    Hi all;
    I need the proof of the folowing Theorem:
    If X is the adjacency matrix of a graph G with n vertices, and
    Y=X+X^2+X^3+....+X^{n-1}, then G is disconnected if and only if there exist at least one entry in matrix Y that is zero.
    Best Wishes
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  2. September 1st 2010, 01:59 AM #2
    Ackbeet
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    What ideas have you had so far?
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