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Zbl 1142.05344
Sciriha, Irene
A characterization of singular graphs.
(English)
[J] Electron. J. Linear Algebra 16, 451-462, electronic only (2007). ISSN 1081-3810/e

Summary: Characterization of singular graphs can be reduced to the non-trivial solutions of a system of linear homogeneous equations ${\bold {Ax=0}}$ for the 0-1 adjacency matrix ${\bold A}$. A graph $G$ is singular of nullity $\eta(G)$ greater than or equal to 1, if the dimension of the nullspace $\text{ker}({\bold A})$ 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 2000:
*05C50 Graphs and matrices

Keywords: adjacency matrix; eigenvalues; singular graphs; core; periphery; singular configuration; minimal configuration

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