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

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Ghodratollah Aalipour
Aida Abiad
Zhanar Berikkyzy
Leslie Hogben
Franklin H.J. Kenter
Jephian C.-H. Lin
Michael Tait

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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