Geodesic
On the maximum positive semi-definite nullity and the cycle matroid of graphs
The electronic journal of linear algebra, Tome 18 (2009), pp. 192-201.

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

Summary: Let G = (V, E) be a graph with $V = {1, 2, . . . , n}$, in which we allow parallel edges but no loops, and let S+ ( G) be the set of all positive semi-definite n $\times n$ matrices A = [a i,j ] with a i,j = 0 if i = j and i and j are non-adjacent, a i,j = 0 if i = j and i and j are connected by exactly one edge, and a i,j $\in R$ if i = j or i and j are connected by parallel edges. The maximum positive semi-definite nullity of G, denoted by M + ( G), is the maximum nullity attained by any matrix A $\in S$ + ( G). A k-separation of G is a pair of subgraphs (G
Classification : 05C50, 15A18
Keywords: positive semi-definite matrices, nullity, graphs, separation, matroids 
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Van Der Holst, Hein. On the maximum positive semi-definite nullity and the cycle matroid of graphs. The electronic journal of linear algebra, Tome 18 (2009), pp. 192-201. http://geodesic.mathdoc.fr/item/ELA_2009__18__a42/