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On the construction of graphs of nullity one. (English) Zbl 0901.05069
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.

05C50Graphs and linear algebra
Full Text: DOI
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