A graph ?$G$? is singular of nullity ?$\eta$? if the nullspace of its adjacency matrix ?${\boldsymbol G}$? has dimension ?$\eta$?. Such a graph contains ?$\eta$? cores determined by a basis for the nullspace of ?${\boldsymbol G}$?. These are induced subgraphs of singular configurations, the latter occurring as induced subgraphs of ?$G$?. We show that there exists a set of ?$\eta$? 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.

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URN

URN:NBN:SI:DOC-YJPF5NNG

COBISSID

15498841

Added

16.12.2021

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Citation

APA:

Sciriha, Irene (2009). Maximal core size in singular graphs. Ars mathematica contemporanea, volume 2, issue 2, str. 217-229. URN:NBN:SI:DOC-YJPF5NNG from http://www.dlib.si

MLA:

Sciriha, Irene. "Maximal core size in singular graphs." Ars mathematica contemporanea volume 2. issue 2 (2009) str. 217-229.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-YJPF5NNG>

Ars mathematica contemporanea
2008-
(Assembly record)