Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree

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

doi:10.13001/1081-3810.3493

Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree

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

^*Corresponding author for this work

QE Operations research

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The conjecture of Graham and Lovasz 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.

Original language	English
Article number	27
Pages (from-to)	373-380
Number of pages	8
Journal	Electronic Journal of Linear Algebra
Volume	34
DOIs	https://doi.org/10.13001/1081-3810.3493
Publication status	Published - 2018

Access to Document

10.13001/1081-3810.3493

http://arxiv.org/pdf/1507.02341Licence: Other

Cite this

@article{1b06216a9f0441a3a3ebbfad3822074e,

title = "Proof of a conjecture of Graham and Lov{\'a}sz concerning unimodality of coefficients of the distance characteristic polynomial of a tree",

abstract = "The conjecture of Graham and Lovasz 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.",

author = "Ghodratollah Aalipour and {Abiad Monge}, Aida and Zhanar Berikkyzy and Leslie Hogben and Kenter, {Franklin H.J.} and Lin, {Jephian C.-H.} and Michael Tait",

note = "data source: no data used",

year = "2018",

doi = "10.13001/1081-3810.3493",

language = "English",

volume = "34",

pages = "373--380",

journal = "Electronic Journal of Linear Algebra",

issn = "1537-9582",

publisher = "International Linear Algebra Society",

}

TY - JOUR

T1 - Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree

AU - Aalipour, Ghodratollah

AU - Abiad Monge, Aida

AU - Berikkyzy, Zhanar

AU - Hogben, Leslie

AU - Kenter, Franklin H.J.

AU - Lin, Jephian C.-H.

AU - Tait, Michael

N1 - data source: no data used

PY - 2018

Y1 - 2018

N2 - The conjecture of Graham and Lovasz 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.

AB - The conjecture of Graham and Lovasz 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.

U2 - 10.13001/1081-3810.3493

DO - 10.13001/1081-3810.3493

M3 - Article

SN - 1537-9582

VL - 34

SP - 373

EP - 380

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

M1 - 27

ER -

Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree

Abstract

Access to Document

Fingerprint

Cite this