Journal or Book Title
Electronic Journal of Linear Algebra
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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Aalipour, Ghodratollah; Abiad, Aida; Berikkyzy, Zhanar; Hogben, Leslie; Kenter, Franklin H.J.; Lin, Jephian C.-H.; and Tait, Michael, "Proof of a Conjecture of Graham and Lovász concerning Unimodality of Coefficients of the Distance Characteristic Polynomial of a Tree" (2018). Mathematics Publications. 235.