The normalized Laplacian, degree-Kirchhoff index and the spanning tree numbers of generalized phenylenes

DOI10.1016/j.dam.2018.06.026zbMath1404.05124OpenAlexW2886205120MaRDI QIDQ1720336

Jia-Bao Liu, Zhongxun Zhu

Publication date: 8 February 2019

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

Full work available at URL: https://doi.org/10.1016/j.dam.2018.06.026

zbMATH Keywords

spanning treenormalized Laplaciandegree-Kirchhoff index

Mathematics Subject Classification ID

Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items

Computation of resistance distance and Kirchhoff index of the two classes of silicate networks, Resistance distance-based graph invariants and spanning trees of graphs derived from the strong prism of a star, The minimum Kirchhoff index of phenylene chains, On sum of powers of normalized Laplacian eigenvalues and resistance distances of graphs, Extremal Kirchhoff index in polycyclic chains, Two-point resistances in the generalized phenylenes, Some resistance distance and distance-based graph invariants and number of spanning trees in the tensor product of P2 and Kn, The (degree-) Kirchhoff indices in random polygonal chains, Extremal bipartite graphs and unicyclic graphs with respect to the eccentric resistance-distance sum, The normalized Laplacians, degree-Kirchhoff index, and the complexity of Möbius graph of linear octagonal-quadrilateral networks, Resistance distance-based graph invariants and the number of spanning trees of linear crossed octagonal graphs, The Kirchhoff index and spanning trees of Möbius/cylinder octagonal chain, On the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks, On the degree Kirchhoff index of unicyclic graphs, On the normalized Laplacian spectral radius, Laplacian incidence energy and Kemeny's constant, On the first three minimum Mostar indices of tree-like phenylenes, Extremal phenylene chains with respect to the Mostar index

Cites Work

• On the resistance matrix of a graph
• Effective resistances and Kirchhoff index of ladder graphs
• The normalized Laplacians, degree-Kirchhoff index and the spanning trees of linear hexagonal chains
• Resistance distance-based graph invariants of subdivisions and triangulations of graphs
• Resistance distance and the normalized Laplacian spectrum
• The normalized Laplacian, degree-Kirchhoff index and spanning trees of the linear polyomino chains
• Resistance characterizations of equiarboreal graphs
• A recursion formula for resistance distances and its applications
• Some results on resistance distances and resistance matrices
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item