Conjectured bounds for the sum of squares of positive eigenvalues of a graph

DOI10.1016/j.disc.2016.01.021zbMath1339.05228arXiv1409.2079OpenAlexW92141041MaRDI QIDQ297913

Felix Goldberg, Clive Elphick, Miriam Farber, Paweł Wocjan

Publication date: 20 June 2016

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.2079

zbMATH Keywords

adjacency matrixhyper-energetic graphsinertia of a graph

Mathematics Subject Classification ID

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

Related Items (8)

Positive and negative square energies of graphs ⋮ Unnamed Item ⋮ Two conjectured strengthenings of Turán's theorem ⋮ Unnamed Item ⋮ Adjacency eigenvalues of graphs without short odd cycles ⋮ Upper bounds for the achromatic and coloring numbers of a graph ⋮ Nordhaus-Gaddum and other bounds for the sum of squares of the positive eigenvalues of a graph ⋮ Eigenvalues and triangles in graphs

Cites Work

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• New spectral bounds on the chromatic number encompassing all eigenvalues of the adjacency matrix
• Proof of a conjectured lower bound on the chromatic number of a graph
• Lower bounds for the clique and the chromatic numbers of a graph
• The energy of graphs and matrices
• Lower bounds on the spectra of symmetric matrices with nonnegative entries
• On graphs with a fixed number of negative eigenvalues
• A bound on the spectral radius of graphs
• Lower bound of the sum of positive eigenvalues of a graph
• Bounds of eigenvalues of graphs
• Some Inequalities for the Largest Eigenvalue of a Graph
• Graphs with Exactly Two Negative Eigenvalues

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