Comparison between Kirchhoff index and the Laplacian-energy-like invariant

DOI10.1016/j.laa.2012.01.002zbMath1241.05072OpenAlexW1980552606MaRDI QIDQ417499

Ivan Gutman, Kexiang Xu, Kinkar Chandra Das

Publication date: 14 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.01.002

zbMATH Keywords

Laplacian-energy-like invariantgraph spectrumKirchhoff indexLaplacian spectrum (of graph)LEL

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (22)

Asymptotic Laplacian-energy-like invariant of lattices ⋮ On extremal bipartite bicyclic graphs ⋮ Generalized characteristic polynomials of join graphs and their applications ⋮ On the Kirchhoff index of the complement of a bipartite graph ⋮ Comparison theorems on resistance distances and Kirchhoff indices of \(S,T\)-isomers ⋮ Ordering connected graphs by their Kirchhoff indices ⋮ On Laplacian-energy-like invariant of a graph ⋮ On the Laplacian-energy-like invariant ⋮ On extremal bipartite unicyclic graphs ⋮ On incidence energy of graphs ⋮ The Laplacian polynomial and Kirchhoff index of graphs derived from regular graphs ⋮ On Laplacian energy of graphs ⋮ Some bounds for the Kirchhoff index of graphs ⋮ Unnamed Item ⋮ Cacti with maximum eccentricity resistance-distance sum ⋮ On sum of powers of the Laplacian eigenvalues of graphs ⋮ Comparison between Laplacian--energy--like invariant and Kirchhoff index ⋮ On Laplacian energy, Laplacian-energy-like invariant and Kirchhoff index of graphs ⋮ On relation between Kirchhoff index, Laplacian-energy-like invariant and Laplacian energy of graphs ⋮ Bounds for Kirchhoff index and Laplacian-energy-like invariant of some derived graphs of a regular graph ⋮ Unnamed Item ⋮ On relations between Kirchhoff index, Laplacian energy, Laplacian-energy-like invariant and degree deviation of graphs

Cites Work

• Resistance distances and the Kirchhoff index in Cayley graphs
• The Laplacian-energy like of graphs
• Ordering of trees with fixed matching number by the Laplacian coefficients
• On the Laplacian coefficients of bicyclic graphs
• Laplacian coefficients of trees with given number of leaves or vertices of degree two
• On the ordering of trees by the Laplacian coefficients
• Laplacian energy of a graph
• Kirchhoff index of composite graphs
• Trees with minimal Laplacian coefficients
• On the Laplacian coefficients of unicyclic graphs
• Ordering trees by the Laplacian coefficients
• Laplacian matrices of graphs: A survey
• On Laplacian like energy of trees
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