Proof of a Conjecture of Graham and Lovász concerning Unimodality of Coefficients of the Distance Characteristic Polynomial of a Tree

Date
2018-08-01
Authors
Aalipour, Ghodratollah
Abiad, Aida
Berikkyzy, Zhanar
Hogben, Leslie
Kenter, Franklin
Lin, Jephian
Tait, Michael
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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.

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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.

Keywords
distance matrix, characteristic polynomial, unimodal, log-concave
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