“School of Mathematics”
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| Paper IPM / M / 7908 |
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| Abstract: | |||||||||
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In this article we show that for any forest there exists a
labelling of the vertices for which the row-reduced echelon form
of its adjacency matrix is a {−1,0,1}-matrix. This result
clearly provides an affirmative answer to the conjecture: The null
space of the adjacency matrix of every forest has a
{−1,0,1}-basis.
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