Kirchhoff indexes of a network

DOI10.1016/j.laa.2009.05.032zbMath1195.94100OpenAlexW1972400840MaRDI QIDQ962118

J. M. Gesto, Enrique Bendito, Margarida Mitjana, Andrés M. Encinas, Ángeles Carmona

Publication date: 6 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.05.032

zbMATH Keywords

eigenvaluesSchrödinger operatorsGreen functionKirchhoff indexeffective resistance

Mathematics Subject Classification ID

Applications of graph theory (05C90) Analytic circuit theory (94C05)

Related Items

Resistance distances on networks, Potential theory on finite networks, The Kirchhoff index of unicycle weighted chains, A novel measure of edge and vertex centrality for assessing robustness in complex networks, Geometry of complex networks and topological centrality, On the Kirchhoff index of the complement of a bipartite graph, Group inverse of the Laplacian of connections of networks, A perturbed averaging operator on finite graphs, The Kirchhoff indexes of some composite networks, Discrete elliptic operators and their Green operators, Bounds for the Kirchhoff index of bipartite graphs, Markov fundamental tensor and its applications to network analysis, A recursion formula for resistance distances and its applications, Resistance distances in extended or contracted networks, Comparison between Laplacian--energy--like invariant and Kirchhoff index, Kirchhoff index of the connections of two networks by an edge, Green matrices associated with generalized linear polyominoes, The Kirchhoff indices of join networks, Bounds for the global cyclicity index of a general network via weighted majorization

Cites Work

• Unnamed Item
• Random walks and the effective resistance of networks
• Resistance distance and the normalized Laplacian spectrum
• Characterization of symmetric \(M\)-matrices as resistive inverses
• A combinatorial Laplacian with vertex weights
• Potential theory for Schrödinger operators on finite networks
• Laplacian eigenvectors of graphs. Perron-Frobenius and Faber-Krahn type theorems
• Bounds on the first nonzero eigenvalue for self-adjoint boundary value problems on networks
• The curl of a weighted network
• Minimizing Effective Resistance of a Graph