Skip to main content
Article
Proof of a Conjecture of Graham and Lovász concerning Unimodality of Coefficients of the Distance Characteristic Polynomial of a Tree
Electronic Journal of Linear Algebra
  • Ghodratollah Aalipour, Kharazmi University
  • Aida Abiad, Tilburg University
  • Zhanar Berikkyzy, Iowa State University
  • Leslie Hogben, Iowa State University
  • Franklin H.J. Kenter, United States Naval Academy
  • Jephian C.-H. Lin, Iowa State University
  • Michael Tait, University of California, San Diego
Document Type
Article
Disciplines
Publication Version
Published Version
Publication Date
8-1-2018
DOI
10.13001/1081-3810.3493
Abstract

The conjecture of Graham and Lovász that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal is proved; it is also shown that the (normalized) coefficients are log-concave. Upper and lower bounds on the location of the peak are established.

Comments

This article is published as Aalipour, Ghodratollah, Aida Abiad, Zhanar Berikkyzy, Leslie Hogben, Franklin Kenter, Jephian C-H. Lin, and Michael Tait. "Proof of a Conjecture of Graham and Lovasz concerning Unimodality of Coefficients of the Distance Characteristic Polynomial of a Tree." The Electronic Journal of Linear Algebra 34 (2018): 373-380. DOI: 10.13001/1081-3810.3493.

Rights
Works produced by employees of the U.S. Government as part of their official duties are not copyrighted within the U.S. The content of this document is not copyrighted.
Language
en
File Format
application/pdf
Citation Information
Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy, Leslie Hogben, et al.. "Proof of a Conjecture of Graham and Lovász concerning Unimodality of Coefficients of the Distance Characteristic Polynomial of a Tree" Electronic Journal of Linear Algebra Vol. 34 (2018) p. 373 - 380
Available at: http://works.bepress.com/leslie-hogben/115/