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Research Article

An explicit upper bound on disparity for trees of a given diameter

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Pages 4584-4596 | Received 01 Sep 2020, Accepted 02 Feb 2021, Published online: 17 Feb 2021

References

  • Leal-Duarte A, Johnson CR. On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree. Math Inequal Appl. 2002;5:175–180.
  • Johnson CR, Saiago CM. Branch duplication for the construction of multiple eigenvalues in an Hermitian matrix whose graph is a tree. Linear Multilinear Algebra. 2008;56:357–380.
  • Johnson CR, Saiago CM. Diameter minimal trees. Linear Multilinear Algebra. 2016;64:557–571.
  • Johnson CR, Lettie J, Mack-Crane S, et al. A. Branch duplication in trees: uniqueness of seeds and enumeration of seeds. Proyecciones. 2020;39:451–465.
  • Ahmadi B, Alinaghipour F, Cavers MS, et al. Minimum number of distinct eigenvalues of graphs. Electron J Linear Algebra. 2013;26:673–691.
  • Barrett W, Fallat S, Hall HT, et al. Generalizations of the strong Arnold property and the minimum number of distinct eigenvalues of a graph. Electron J Combin. 2017;24(2):1–28. Paper 2.40.
  • Johnson CR, Saiago CM, Eigenvalues, multiplicities and graphs. New York (NY): Cambridge University Press; 2018.

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