On the second largest adjacency eigenvalue of trees with given diameter

2024/09/02 by Hitesh Kumar, Kumar, Hitesh, Bojan Mohar +5
Mathematics · Chemistry · #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.2409.01431

Abstract

For a graph G, let λ₂(G) denote the second largest eigenvalue of the adjacency matrix of G. We determine the extremal trees with maximum/minimum adjacency eigenvalue λ₂ in the class T(n,d) of n-vertex trees with diameter d. This contributes to the literature on λ₂-extremization over different graph families. We also revisit the notion of the spectral center of a tree and the proof of λ₂ maximization over trees.

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