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Laplacian spectral characterization of two families of trees

Aalipour, G ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1080/03081087.2013.801966
  3. Abstract:
  4. It is well known that all starlike trees, i.e. trees with exactly one vertex of degree at least three, are determined by their Laplacian spectrum. A double starlike tree is a tree with exactly two vertices of degree at least three. In 2009, the following question was posed: Are all the double starlike trees determined by their Laplacian spectra? In this direction, it was proved that one special double starlike tree Hn(p,p) is determined by its Laplacian spectrum, where Hn(p,q) is a tree obtained by joining p pendant vertices to an end vertex of a path of order and then joining pendant vertices to another end of the path. Also, the banana tree Bn,k is a tree obtained by joining a vertex to one arbitrary pendant vertex of each copy of n-copies of K1,k. Recently, it is shown that Hn(p, p-1) is determined by its Laplacian spectrum as well. In this paper, we study the Laplacian spectral characterization of Hn(p,q) and Bn,k. We show that Bp,q and Hn(p,q) are determined by their Laplacian spectra, for p2 ≤ q
  5. Keywords:
  6. Laplacian spectrum ; Tree
  7. Source: Linear and Multilinear Algebra ; Volume 62, Issue 7 , July , 2014 , Pages 965-977 ; ISSN: 03081087
  8. URL: http://www.tandfonline.com/doi/abs/10.1080/03081087.2013.801966#.VZuakcldKak