On the Wiener index, distance cospectrality and transmission-regular graphs

DOI10.1016/j.dam.2017.07.010zbMath1368.05035arXiv1609.06911OpenAlexW2963093437MaRDI QIDQ2399284

Aysel Erey, Suil O, Lorinda Leshock, Aida Abiad, Boris Brimkov, Sung-Yell Song, Xavier Martinez-Rivera, Jason S. Williford

Publication date: 22 August 2017

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

Full work available at URL: https://arxiv.org/abs/1609.06911

zbMATH Keywords

diameterLaplacian matrixWiener indexdistance matrixdistance cospectral graphstransmission-regular

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distance in graphs (05C12)

Related Items (24)

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Uses Software

• OEIS

Cites Work

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• Orientations of graphs with maximum Wiener index
• Average distance in weighted graphs
• Algorithms for graphs of bounded treewidth via orthogonal range searching
• Forbidden minors for the class of graphs \(G\) with \(\xi (G) \leqslant 2\)
• Three-connected graphs whose maximum nullity is at most three
• Sharp bounds on the distance spectral radius and the distance energy of graphs
• On distance-balanced graphs
• A characterization of block graphs
• Strongly distance-balanced graphs and graph products
• Eigenvalues, diameter, and mean distance in graphs
• Minimal acyclic forbidden minors for the family of graphs with bounded path-width
• Distance spectra of graphs: a survey
• A construction of distance cospectral graphs
• Subclasses of \(k\)-trees: characterization and recognition
• Mathematical aspects of Wiener index
• Distance spectrum of graph compositions
• An edge version of the matrix-tree theorem and the wiener index
• The distance spectrum of a tree
• The graphs for which the maximum multiplicity of an eigenvalue is two
• Parameters Related to Tree‐Width, Zero Forcing, and Maximum Nullity of a Graph
• Estimating the distance Estrada index
• Minimizing Wiener Index for Vertex-Weighted Trees with Given Weight and Degree Sequences
• Contraction Formulas For Kirchhoff And Wiener Indices
• On the Addressing Problem for Loop Switching
• Wiener index of trees: Theory and applications

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