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Paper   IPM / M / 11365
School of Mathematics
  Title:   A note on graphs whose signless Laplacian has three distinct eigenvalues
1.  G. R. Omidi
2.  B. Tayfeh-Rezaie (Joint with F. Ayoobi)
  Status:   Published
  Journal: Linear Multilinear Algebra
  Vol.:  59
  Year:  2011
  Pages:   701-706
  Supported by:  IPM
We investigate graphs whose signless Laplacian matrix has three distinct eigenvalues. We show that the largest signless Laplacian eigenvalue of a connected graph G with three distinct signless Laplacian eigenvalues is noninteger if and only if G=Kne for n ≥ 4, where Kne is the n vertex complete graph with an edge removed. Moreover, examples of such graphs are given.

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