Principal minors of the distance matrix of a tree

2024/07/02 by Álvaro Gómez‐Gutiérrez, Gutiérrez, Álvaro, Adrián Lillo +1
Computer Science · Mathematics · #05A15 (Secondary) #05C05 (Primary) 05A19 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2407.01966

openalex publication_date 2024/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let T = ([n], E) be a tree and let D = ( d(i,j) )_{i, j ≤ n} be the distance matrix of T. Let S⊆ [n]. We give the first combinatorial proof for a formula to compute the principal minor of D indexed by S, namely det D[S]. This generalizes work of Graham and Pollak, as well as more recent works.

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