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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.)