Geodesic
Maximal core size in singular graphs
Ars Mathematica Contemporanea, Tome 2 (2009) no. 2, pp. 217-229.

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A graph G is singular of nullity η if the nullspace of its adjacency matrix G has dimension η. Such a graph contains η cores determined by a basis for the nullspace of G. These are induced subgraphs of singular configurations, the latter occurring as induced subgraphs of G. We show that there exists a set of η distinct vertices representing the singular configurations. We also explore how the nullity controls the size of the singular substructures and characterize those graphs of maximal nullity containing a substructure reaching maximal size.
DOI : 10.26493/1855-3974.115.891
Keywords: adjacency matrix, singular graphs, nullity, extremal singular graphs, singular congurations, core width 
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Irene Sciriha. Maximal core size in singular graphs. Ars Mathematica Contemporanea, Tome 2 (2009) no. 2, pp. 217-229. doi : 10.26493/1855-3974.115.891. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.115.891/

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