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On the construction of graphs of nullity one. (English) Zbl 0901.05069
The author classifies the sets of \(k\) \((2\leq k\leq 5)\) 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.

MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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