The extremal \(\alpha \)-index of outerplanar and planar graphs

DOI10.1016/j.amc.2018.09.043zbMath1428.05211OpenAlexW2896965117MaRDI QIDQ2008179

Erfang Shan, Zhangqing Yu, Lele Liu, Li-ying Kang

Publication date: 22 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.09.043

zbMATH Keywords

planar graphouterplanar graphconvex combination of matrices\( \alpha \)-indexspectral extremal problem

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (13)

On the \(A_\alpha\)- spectral radius of Halin graphs ⋮ On the multiplicity of an arbitrary \(A_\alpha\)-eigenvalue of a connected graph ⋮ A complete solution to the Cvetković–Rowlinson conjecture ⋮ Aα-spectrum of duplicate and corona operations in graphs ⋮ On the \(A_\alpha\)-spectral radius of graphs without linear forests ⋮ The \(A_\alpha\)-spread of a graph ⋮ Unnamed Item ⋮ The extremal \(\alpha \)-index of graphs with no 4-cycle and 5-cycle ⋮ On the second largest \(A_{\alpha}\)-eigenvalues of graphs ⋮ \(a_\alpha \)-spectral radius of the second power of a graph ⋮ The Nordhaus-Gaddum type inequalities of \(A_\alpha \)-matrix ⋮ On the multiplicity of \(\alpha\) as an eigenvalue of the \(a_\alpha\) matrix of a graph in terms of the number of pendant vertices ⋮ The sharp upper bounds on the \(A_{\alpha}\)-spectral radius of \(C_4\)-free graphs and Halin graphs

Cites Work

• The edge-density for \(K_{2,t}\) minors
• Three conjectures in extremal spectral graph theory
• The spectral radius of graphs with no \(k_{2,t}\) minor
• Merging the A-and Q-spectral theories

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