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Displaying similar documents to “Eigenvalue Conditions for Induced Subgraphs”

An upper bound on the Laplacian spectral radius of the signed graphs

Hong-Hai Li, Jiong-Sheng Li (2008)

Discussiones Mathematicae Graph Theory

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In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.

On the second largest eigenvalue of a mixed graph

Jun Zhou, Yi-Zheng Fan, Yi Wang (2007)

Discussiones Mathematicae Graph Theory

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Let G be a mixed graph. We discuss the relation between the second largest eigenvalue λ₂(G) and the second largest degree d₂(G), and present a sufficient condition for λ₂(G) ≥ d₂(G).

On the inverse eigenvalue problem for a special kind of acyclic matrices

Mohammad Heydari, Seyed Abolfazl Shahzadeh Fazeli, Seyed Mehdi Karbassi (2019)

Applications of Mathematics

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We study an inverse eigenvalue problem (IEP) of reconstructing a special kind of symmetric acyclic matrices whose graph is a generalized star graph. The problem involves the reconstruction of a matrix by the minimum and maximum eigenvalues of each of its leading principal submatrices. To solve the problem, we use the recurrence relation of characteristic polynomials among leading principal minors. The necessary and sufficient conditions for the solvability of the problem are derived....