DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

Discussiones Mathematicae Graph Theory

Article in press


Authors:

N. Abreu, J. Alencar, A. Brondani, L. de Lima, C. Oliveira

Title:

Graphs with all but two eigenvalues in [$-2,0$]

Source:

Discussiones Mathematicae Graph Theory

Received: 2019-04-07, Revised: 2019-10-11, Accepted: 2019-11-20, https://doi.org/10.7151/dmgt.2286

Abstract:

The eigenvalues of a graph are those of its adjacency matrix. Recently, Cioabă, Haemers and Vermette characterized all graphs with all but two eigenvalues equal to $ -2$ and $0.$ In this article, we extend their result by characterizing explicitly all graphs with all but two eigenvalues in the interval $[-2, 0].$ Also, we determine among them those that are determined by their spectrum.

Keywords:

graph spectrum, complete multipartite graph, graph determined by its spectrum

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