Trees with extremal spectral radius of weighted adjacency matrices among trees weighted by degree-based indices

DOI10.1016/j.laa.2021.02.023zbMath1462.05232OpenAlexW3134848558MaRDI QIDQ2020676

Zhiqian Wang, Xue Liang Li

Publication date: 24 April 2021

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2021.02.023

zbMATH Keywords

spectral radiusweighted adjacency matrixextremal treetrees weighted by degree-based indices

Mathematics Subject Classification ID

Trees (05C05) Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Vertex degrees (05C07) Graphical indices (Wiener index, Zagreb index, Randi? index, etc.) (05C09) Chemical graph theory (05C92)

Related Items (18)

Some Degree-Based Topological Indices and (Normalized Laplacian) Energy of Graphs ⋮ Extremal Graphs for Topological Index Defined by a Degree-Based Edge-Weight Function ⋮ Extremal Problems for Graphical Function-Indices and f-Weighted Adjacency Matrix ⋮ Sombor Energy and Hückel Rule ⋮ Extremal problems on sombor indices of unicyclic graphs with a given diameter ⋮ Sombor index: review of extremal results and bounds ⋮ On the spectral radius, energy and Estrada index of the Sombor matrix of graphs ⋮ Generation matrix: an embeddable matrix representation for hierarchical trees ⋮ Extremal trees and unicyclic graphs with respect to spectral radius of weighted adjacency matrices with property \(P^*\) ⋮ Extreme Sombor Spectral Radius of Unicyclic Graphs ⋮ Relationship between Ordinary, Laplacian, Randić, Incidence, and Sombor Energies of Trees ⋮ The effect on the largest eigenvalue of degree-based weighted adjacency matrix by perturbations ⋮ Some interlacing results on weighted adjacency matrices of graphs with degree-based edge-weights ⋮ Unnamed Item ⋮ Degree-based energies of trees ⋮ A relation between a vertex-degree-based topological index and its energy ⋮ Energy of a digraph with respect to a VDB topological index ⋮ Unnamed Item

Cites Work

• Spectra of graphs
• Degree-based energies of graphs
• The asymptotic value of graph energy for random graphs with degree-based weights
• On extremality of ABC spectral radius of a tree
• The balanced double star has maximum exponential second Zagreb index
• Trees with maximum exponential Randić index
• The asymptotic value of energy for matrices with degree-distance-based entries of random graphs
• Asymptotic values of four Laplacian-type energies for matrices with degree-distance-based entries of random graphs
• On the eigenvalue and energy of extended adjacency matrix
• Extremal values of vertex-degree-based topological indices over graphs
• On graphs with randomly deleted edges
• The maximal tree with respect to the exponential of the second Zagreb index
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