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

Aalipour, Ghodratollah; Abiad, Aida; Berikkyzy, Zhanar; Hogben, Leslie; Hogben, Leslie; Kenter, Franklin; Lin, Jephian; Tait, Michael

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

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2018_HogbenLeslie_ProofConjecture.pdf (846.34 KB)

Date

2018-08-01

Authors

Aalipour, Ghodratollah

Abiad, Aida

Berikkyzy, Zhanar

Hogben, Leslie

Kenter, Franklin

Lin, Jephian

Tait, Michael

Authors

Person

Hogben, Leslie

Associate Dean

Organizational Units

Organizational Unit

Electrical and Computer Engineering

The Department of Electrical and Computer Engineering (ECpE) contains two focuses. The focus on Electrical Engineering teaches students in the fields of control systems, electromagnetics and non-destructive evaluation, microelectronics, electric power & energy systems, and the like. The Computer Engineering focus teaches in the fields of software systems, embedded systems, networking, information security, computer architecture, etc.

History
The Department of Electrical Engineering was formed in 1909 from the division of the Department of Physics and Electrical Engineering. In 1985 its name changed to Department of Electrical Engineering and Computer Engineering. In 1995 it became the Department of Electrical and Computer Engineering.

Dates of Existence
1909-present

Historical Names

Department of Electrical Engineering (1909-1985)
Department of Electrical Engineering and Computer Engineering (1985-1995)

Related Units

College of Engineering (parent college)
Department of Physics and Electrical Engineering (predecessor)

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Mathematics

Welcome to the exciting world of mathematics at Iowa State University. From cracking codes to modeling the spread of diseases, our program offers something for everyone. With a wide range of courses and research opportunities, you will have the chance to delve deep into the world of mathematics and discover your own unique talents and interests. Whether you dream of working for a top tech company, teaching at a prestigious university, or pursuing cutting-edge research, join us and discover the limitless potential of mathematics at Iowa State University!

Department

Electrical and Computer EngineeringMathematics

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.

Comments

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.