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

2015/07/08 by Ghodratollah Aalipour, Aida Abiad, Aalipour, Ghodratollah +13
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis #math.CO

paper · pdf · doi:10.48550/arxiv.1507.02341

openalex publication_date 2015/07/08 · arxiv created 2017/04/20 · arxiv updated 2017/04/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We establish a conjecture of Graham and Lovász that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal; we also prove they are log-concave.

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• Multiple breaks of log-concavity in the independence polynomials of trees