On extremal bipartite unicyclic graphs

DOI10.1016/j.laa.2013.11.038zbMath1292.05144OpenAlexW2020163967MaRDI QIDQ2442249

Qingying Deng, Hai-Yan Chen

Publication date: 2 April 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2013.11.038

zbMATH Keywords

Estrada indexKirchhoff indexcomplement graphclosed walkbipartite unicyclic graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (20)

Graphs with maximum Laplacian and signless Laplacian Estrada index ⋮ On extremal bipartite bicyclic graphs ⋮ Some extremal properties of the resolvent energy, Estrada and resolvent Estrada indices of graphs ⋮ Extremal graphs of bipartite graphs of given diameter for two indices on resistance-distance ⋮ More on the Estrada indices of trees ⋮ Statistical analyses of a class of random pentagonal chain networks with respect to several topological properties ⋮ On the Kirchhoff index of bipartite graphs with given diameters ⋮ The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications ⋮ Complete characterization of bicyclic graphs with minimal Kirchhoff index ⋮ On the ordering of the Kirchhoff indices of the complements of trees and unicyclic graphs ⋮ Some bounds for the Kirchhoff index of graphs ⋮ Resistance distance-based graph invariants of subdivisions and triangulations of graphs ⋮ The Kirchhoff indices and the matching numbers of unicyclic graphs ⋮ Minimizing Kirchhoff index among graphs with a given vertex bipartiteness ⋮ On the minimum Kirchhoff index of graphs with a given vertex \(k\)-partiteness and edge \(k\)-partiteness ⋮ Theoretical and computational methods to minimize Kirchhoff index of graphs with a given edge \(k\)-partiteness ⋮ Extremal Estrada indices of the weighted trees with fixed total weight sum ⋮ Minimal Estrada Indices of the Trees with a Perfect Matching ⋮ Comparison of the Wiener and Kirchhoff indices of random pentachains ⋮ On the Estrada index of cactus graphs

Cites Work

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• On the Kirchhoff index of the complement of a bipartite graph
• Resistance distances and the Kirchhoff index in Cayley graphs
• The Estrada index of unicyclic graphs
• Comparison between Kirchhoff index and the Laplacian-energy-like invariant
• Bounds for the Kirchhoff index of bipartite graphs
• On a poset of trees
• On the Estrada and Laplacian Estrada indices of graphs
• On Estrada index of trees
• On the Estrada index conjecture
• The Estrada index of chemical trees
• Walks and paths in trees
• A connection between ordinary and Laplacian spectra of bipartite graphs

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