A proof of a conjecture on the distance spectral radius

2023/03/17 by Yanna Wang, Bo Zhou, Wang, Yanna +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Optimization Algorithms Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2303.09742

openalex publication_date 2023/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A cactus is a connected graph in which any two cycles have at most one common vertex. We determine the unique graph that maximizes the distance spectral radius over all cacti with fixed numbers of vertices and cycles, and thus prove a conjecture on the distance spectral radius of cacti in [S.S. Bose, M. Nath, S. Paul, On the distance spectral radius of cacti, Linear Algebra Appl. 437 (2012) 2128--2141]. We prove the result in the context of hypertrees.

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