distance matrix, characteristic polynomial, unimodal, log-concave
The conjecture of Graham and Lov ́asz 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.
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 Lovasz concerning Unimodality of Coefficients of the Distance Characteristic Polynomial of a Tree",
Electronic Journal of Linear Algebra,
Volume 34, pp. 373-380.