Connected graphs of fixed order and size with maximal index: some spectral bounds

DOI10.1016/j.laa.2009.06.043zbMath1217.05157OpenAlexW2051481353MaRDI QIDQ962125

Dejan V. Tošić, Francesco Belardo, Enzo Maria Li Marzi, Slobodan K. Simic

Publication date: 6 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.06.043

zbMATH Keywords

spectral radiuslargest eigenvaluethreshold graphadjacency spectrumnested split graphspectral boundsgraph index

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (12)

No threshold graphs are cospectral ⋮ Connected graphs of fixed order and size with maximal \(Q\)-index: some spectral bounds ⋮ An explicit formula for the distance characteristic polynomial of threshold graphs ⋮ Connected graphs of fixed order and size with maximal \(A_\alpha \)-index: the one-dominating-vertex case ⋮ Sharp bounds on the \(A_{\alpha}\)-index of graphs in terms of the independence number ⋮ Eigenvalue location in threshold graphs ⋮ Maximize the \(Q\)-index of graphs with fixed order and size ⋮ Efficient computation of the characteristic polynomial of a threshold graph ⋮ Some spectral inequalities for connected bipartite graphs with maximum \(A_\alpha\)-index ⋮ On bounds for the index of double nested graphs ⋮ An extremal problem on Q-spectral radii of graphs with given size and matching number ⋮ Some bounds on the A_α-index of connected graphs with fixed order and size

Cites Work

• Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph
• On the spectral radius of (0,1)-matrices
• The maximal eigenvalue of 0-1 matrices with prescribed number of ones
• Bounds on the spectral radius of graphs with e edges
• On the maximal index of graphs with a prescribed number of edges
• A bound on the spectral radius of graphs with \(e\) edges
• The largest eigenvalue of a graph: A survey
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