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Paper   IPM / M / 7908
School of Mathematics
  Title:   {−1,0,1}-basis for the null space of a forest
1.  S. Akbari
2.  A. Alipour
3.  E. Ghorbani
4.  G. B. Khosrovshahi
  Status:   Published
  Journal: Linear Algebra Appl.
  Vol.:  414
  Year:  2006
  Pages:   506-511
  Supported by:  IPM
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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