Aida Abiad

Some spectral and quasi-spectral characterizations of distance-regular graphs

In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using the preintersection numbers we give some new spectral and quasi-spectral characterizations of distance-regularity, in particular for graphs with large girth or large odd-girth.

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

In this paper, we investigate various algebraic and graph theoretic properties of the distance matrix of a graph. Two graphs are

Algebraic characterizations of regularity properties in bipartite graphs

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Switched symplectic graphs and their 2-ranks

-cospectral if their distance matrices have the same spectrum. We construct infinite pairs of

Corrigendum: Corrigendum to Algebraic characterizations of regularity properties in bipartite graphs [European J. Combin. 34 (2013) 1223-1231]

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A characterization of weight-regular partitions of graphs

-cospectral graphs with different diameter and different Wiener index. A graph is

On the Distance Spectra of Graphs

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GODSIL-MCKAY SWITCHING AND ISOMORPHISM

-transmission-regular if its distance matrix has constant row sum equal to

An application of Hoffman graphs for spectral characterizations of graphs

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Proof of a Conjecture of Graham and Lovasz concerning Unimodality of Coefficients of the Distance Characteristic Polynomial of a Tree

. We establish tight upper and lower bounds for the row sum of a