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

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

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

21 Citaten (Scopus)


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.

Originele taal-2Engels
Pagina's (van-tot)1-10
Aantal pagina's10
TijdschriftDiscrete Applied Mathematics
StatusGepubliceerd - 30 okt 2017
Extern gepubliceerdJa


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