Geodesic
A characterization of singular graphs
The electronic journal of linear algebra, Tome 16 (2007), pp. 451-462.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 ${ker}({\bold A})$ 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.
Classification : 05C50, 05C60, 05B20
Keywords: adjacency matrix, eigenvalues, singular graphs, core, periphery, singular configuration, minimal configuration 
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Sciriha, Irene. A characterization of singular graphs. The electronic journal of linear algebra, Tome 16 (2007), pp. 451-462. http://geodesic.mathdoc.fr/item/ELA_2007__16__a0/