The Kirchhoff indices of join networks

DOI10.1016/j.dam.2011.09.017zbMath1237.05123OpenAlexW2084389042MaRDI QIDQ765336

Ángeles Carmona, Enrique Bendito, Andrés M. Encinas

Publication date: 19 March 2012

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

Full work available at URL: https://doi.org/10.1016/j.dam.2011.09.017

zbMATH Keywords

Green's functionKirchhoff indexeffective resistancejoin networkSchrödinger spectrum

Mathematics Subject Classification ID

Applications of graph theory (05C90) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Discrete potential theory (31C20)

Related Items (8)

Laplacian matrix of a weighted graph with new pendant vertices ⋮ On the resistance distance and Kirchhoff index of a linear hexagonal (cylinder) chain ⋮ Green functions on product networks ⋮ Group inverse of the Laplacian of connections of networks ⋮ Group inverses of a class of corona networks ⋮ Discrete elliptic operators and their Green operators ⋮ Further results on resistance distance and Kirchhoff index in electric networks ⋮ Green operators of networks with a new vertex

Cites Work

• Kirchhoff indexes of a network
• Kirchhoff index of composite graphs
• Resistance distance in wheels and fans
• Characterization of symmetric \(M\)-matrices as resistive inverses
• Potential theory for Schrödinger operators on finite networks
• Laplacian eigenvectors of graphs. Perron-Frobenius and Faber-Krahn type theorems
• The curl of a weighted network
• Eigenvalues, eigenfunctions and Green's functions on a path via Chebyshev polynomials
• Minimizing Effective Resistance of a Graph

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