×

zbMATH — the first resource for mathematics

A characterization of singular graphs. (English) Zbl 1142.05344
Summary: Characterization of singular graphs can be reduced to the non-trivial solutions of a system of linear homogeneous equations \({\mathbf {Ax=0}}\) for the 0-1 adjacency matrix \({\mathbf A}\). A graph \(G\) is singular of nullity \(\eta(G)\) greater than or equal to 1, if the dimension of the nullspace \(\text{ker}({\mathbf A})\) of its adjacency matrix \(A\) is \(\eta(G)\). Necessary and sufficient conditions are determined for a graph to be singular in terms of admissible induced subgraphs.

MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
PDF BibTeX XML Cite
Full Text: DOI Link EuDML