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Zbl 0901.05069
Sciriha, Irene
On the construction of graphs of nullity one. (English)
[J] Discrete Math. 181, No.1-3, 193-211 (1998). ISSN 0012-365X

The author classifies the sets of $k$ $(2\le k\le 5)$ linearly dependent rows of the adjacency matrix of a graph. Induced subgraphs related to these sets can be of some help in determining the multiplicity of the eigenvalue $0$. Some constructions of graphs having eigenvalue $0$ in the spectrum are given as well.
[D.Cvetković (Beograd)]

MSC 2000:: *05C50 Graphs and matrices

Keywords: adjacency matrix; eigenvalue

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