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Paper   IPM / M / 8737
School of Mathematics
  Title:   Graphs cospectral with starlike trees
1.  N. Ghareghani
2.  F. Ramezani
3.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: Linear Algebra Appl.
  Vol.:  429
  Year:  2008
  Pages:   2691-2701
  Supported by:  IPM
A tree which has exactly one vertex of degree greater than two is said to be starlike. In spite of seemingly simple structure of these trees, not much is known about their spectral properties. In this paper, we introduce a generalization of the notion of cospectrality called m-cospectrality which turns out to be useful in constructing cospectral graphs. Based on this, we construct cospectral mates for some starlike trees. We also present a set of necessary and sufficient conditions for divisibility of the characteristic polynomial of a starlike tree by the characteristic polynomial of a path.

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