Extending a conjecture of Graham and Lovász on the distance characteristic polynomial

2022/06/15 by Aida Abiad, Boris Brimkov, Abiad, Aida +7
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2206.07561

openalex publication_date 2022/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order n is unimodal with the maximum value occurring at \lfloor(n)/(2)\rfloor. In this paper we investigate this problem for block graphs. In particular, we prove the unimodality part and we establish the peak for several extremal cases of uniform block graphs with small diameter.

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