Bicyclic graphs with exactly two main eigenvalues

DOI10.1016/j.laa.2009.06.022zbMath1175.05085OpenAlexW2049876479MaRDI QIDQ732075

Shuchao Li, Chunfeng Zhu, Zhi-quan Hu

Publication date: 9 October 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.06.022

zbMATH Keywords

bicyclic graphsmain eigenvalues2-walk linear graphsspectra of a graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (15)

A note on graphs with exactly two main eigenvalues ⋮ A bound on the spectral radius of graphs in terms of their Zagreb indices ⋮ Trees, unicyclic graphs and bicyclic graphs with exactly two \(Q\)-main eigenvalues ⋮ Tricyclic graphs with exactly two main eigenvalues ⋮ Some results on graphs with exactly two main eigenvalues ⋮ On the main spectrum of generalized Bethe trees ⋮ Unicyclic and bicyclic graphs with exactly three \(Q\)-main eigenvalues ⋮ Construction of graphs with exactly \(k\) main eigenvalues ⋮ Construction of graphs with distinct eigenvalues ⋮ 2-Walk linear graphs with small number of cycles ⋮ Some structural properties of 2-walk (a, b)-linear graphs ⋮ On graphs with exactly three Q-main eigenvalues ⋮ A few examples and counterexamples in spectral graph theory ⋮ Some new aspects of main eigenvalues of graphs ⋮ On main eigenvalues of chain graphs

Cites Work

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• A table of connected graphs on six vertices
• Semiharmonic bicyclic graphs
• Unicyclic graphs with exactly two main eigenvalues
• The number of walks in a graph
• Semiharmonic graphs with fixed cyclomatic number.
• Some results on graph spectra
• Harmonic trees
• Harmonic graphs with small number of cycles

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