Graphs whose distance matrix has at most three negative eigenvalues

Graphs whose distance matrix has at most three negative eigenvalues

Let D(G) be the distance matrix of a connected simple graph G. The negative inertia of D(G), denoted by nD(G), is the number of negative eigenvalues of D(G). In this paper, we determine all connected graphs G whose distance matrix D(G) has at most three negative eigenvalues.

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Bibliographische Detailangaben
Veröffentlicht in:Linear algebra and its applications 2017-10, Vol.530, p.470-484
Hauptverfasser: Tian, Fenglei, Wong, Dein
Format: Artikel
Sprache:eng
Schlagworte:
D-eigenvalue
Distance matrix
Eigenvalues
Graph theory
Graphs
Linear algebra
Matrix
Negative inertia
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Zusammenfassung:Let D(G) be the distance matrix of a connected simple graph G. The negative inertia of D(G), denoted by nD(G), is the number of negative eigenvalues of D(G). In this paper, we determine all connected graphs G whose distance matrix D(G) has at most three negative eigenvalues.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.05.040