On ABC eigenvalues and ABC energy

DOI10.1016/j.laa.2018.01.011zbMath1388.05112OpenAlexW2783746350MaRDI QIDQ1637992

Xiaodan Chen

Publication date: 12 June 2018

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.01.011

zbMATH Keywords

ABC indexABC eigenvaluesABC energyABC matrix

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Vertex degrees (05C07)

Related Items (20)

Inverse sum Indeg index and ISI matrix of graphs ⋮ On the Zagreb matrix and Zagreb energy ⋮ A note on the ABC spectral radius of graphs ⋮ Bounds on the \(ABC\) spectral radius and \(ABC\) energy of graphs ⋮ On the eigenvalues of Laplacian ABC -matrix of graphs ⋮ On the ABC spectral radius of cactus graphs ⋮ Generalized ABC energy of weighted graphs ⋮ The minimum exponential atom-bond connectivity energy of trees ⋮ Arithmetic-geometric matrix of graphs and its applications ⋮ Some interlacing results on weighted adjacency matrices of graphs with degree-based edge-weights ⋮ On extremality of ABC spectral radius of a tree ⋮ The first two maximum ABC spectral radii of bicyclic graphs ⋮ On ABC Estrada index of graphs ⋮ The minimum ABC energy of trees ⋮ On large ABC spectral radii of unicyclic graphs ⋮ Bounds on the ABC spectral radius of a tree ⋮ On the ABC spectra radius of unicyclic graphs ⋮ Nordhaus-Gaddum-type relations for arithmetic-geometric spectral radius and energy ⋮ On the Randić matrix and Randić energy ⋮ Atom–bond connectivity index of graphs: a review over extremal results and bounds

Cites Work

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• Some upper bounds for the atom-bond connectivity index of graphs
• Further results on atom-bond connectivity index of trees
• On atom-bond connectivity index of connected graphs
• The ABC matrix
• Atom-bond connectivity index of graphs
• Atom-bond connectivity index of trees
• On the normalized Laplacian energy and general Randić index \(R_{-1}\) of graphs
• Bounds on Randić indices
• Augmented Zagreb index
• Some inequalities for the atom-Bond connectivity index of graph operations
• General Randić matrix and general Randić incidence matrix
• Computer search for trees with minimal ABC index
• The ABC index conundrum

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