Geodesic
On the nullity of graphs
The electronic journal of linear algebra, Tome 16 (2007), pp. 60-67.

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

Summary: The nullity of a graph $G$, denoted by $\eta(G)$, is the multiplicity of the eigenvalue zero in its spectrum. It is known that $\eta(G)\le n-2$ if $G$ is a simple graph on $n$ vertices and $G$ is not isomorphic to $nK_1$. In this paper, we characterize the extremal graphs attaining the upper bound $n-2$ and the second upper bound $n-3$. The maximum nullity of simple graphs with $n$ vertices and $e$ edges, $M(n,e)$, is also discussed. We obtain an upper bound of $M(n,e)$, and characterize $n$ and $e$ for which the upper bound is achieved.
Classification : 05C50
Keywords: graph eigenvalue, nullity, clique, girth, diameter 
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Cheng, Bo; Liu, Bolian. On the nullity of graphs. The electronic journal of linear algebra, Tome 16 (2007), pp. 60-67. http://geodesic.mathdoc.fr/item/ELA_2007__16__a33/