On the construction of graphs of nullity one
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.
scientific article; zbMATH DE number 1135965