Maximum generic nullity of a graph

Maximum Generic Nullity of a Graph

For a graph G of order n, the maximum nullity of G is defined to be the largest possible nullity over all real symmetric n × n matrices A whose (i, j)th entry (for i 6= j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity and the related parameter minimum rank of the same set of matrices have been studied extensively. A new parameter, maximum generic nullity, is ...

Generic maximum nullity of a graph

For a graph G of order n, the maximum nullity of G is defined to be the largest possible nullity over all real symmetric n × n matrices A whose (i, j)th entry (for i 6= j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity and the related parameter minimum rank of the same set of matrices have been studied extensively. A new parameter, generic maximum nullity, is ...

Ela the Maximum Nullity of a Complete Subdivision Graph Is Equal to Its Zero Forcing Number∗

Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all complete subdivision graphs. We prove that this equality holds. Furthermore, we compute the value of M(F, G̊) = Z(G̊) by introducing the bridge tree of a connected graph. Since this...

Parameters Related to Tree-Width, Zero Forcing, and Maximum Nullity of a Graph

Tree-width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by a graph. We establish relationships between these parameters, including several Colin de Verdière type...

The Maximum Number of Edges in a Strongly Multiplicative Graph