Research output

On the Wiener index, distance cospectrality and transmission regular graphs

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Associated researcher

  • Abiad Monge, A.

  • Brimkov, B.
  • Erey, A.
  • Leshock, L.
  • Martínez-Rivera, X.
  • O, S.
  • Song, S.
  • Williford, J.

Associated organisations

Abstract

In this paper, we investigate various algebraic and graph theoretic properties of the distance matrix of a graph. Two graphs are D-cospectral if their distance matrices have the same spectrum. We construct infinite pairs of D-cospectral graphs with different diameter and different Wiener index. A graph is k-transmission-regular if its distance matrix has constant row sum equal to k. We establish tight upper and lower bounds for the row sum of a k-transmission-regular graph in terms of the number of vertices of the graph. Finally, we determine the Wiener index and its complexity for linear k-trees, and obtain a closed form for the Wiener index of block-clique graphs in terms of the Laplacian eigenvalues of the graph. The latter leads to a generalization of a result for trees which was proved independently by Mohar and Merris. (C) 2017 Elsevier B.V. All rights reserved.

    Research areas

  • Distance matrix, Distance cospectral graphs, Diameters, Wiener index, Laplacian matrix, Transmission-regular, BALANCED GRAPHS, MATRIX, NUMBER, LARGEST EIGENVALUE, WIDTH, FORBIDDEN MINORS, TREES, SPECTRUM, VERTICES, Diameter
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Details

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalDiscrete Applied Mathematics
Volume230
DOIs
Publication statusPublished - 30 Oct 2017