Home > ELA > Vol. 30 (2015)

#### Keywords

Zero forcing, Inertia sets, Isotropic subspaces

#### Abstract

Zero forcing is a combinatorial game played on a graph with a goal of changing the color of every vertex at minimal cost. This leads to a parameter known as the zero forcing number that can be used to give an upper bound for the maximum nullity of a matrix associated with the graph. A variation on the zero forcing game is introduced that can be used to give an upper bound for the maximum nullity of such a matrix when it is constrained to have exactly q negative eigenvalues. This constrains the possible inertias that a matrix associated with a graph can achieve and gives a method to construct lower bounds on the inertia set of a graph (which is the set of all possible pairs (p,q) where p is the number of positive eigenvalues and q is the number of negative eigenvalues).

#### Recommended Citation

Butler, Steve; Grout, Jason; and Hall, H. Tracy.
(2015),
"Using variants of zero forcing to bound the inertia set of a graph",
*Electronic Journal of Linear Algebra*,
Volume 30.

DOI: http://dx.doi.org/10.13001/1081-3810.2900