Publications (7)
A construction of cospectral graphs for the normalized Laplacian
Steve Butler, Jason Grout
We give a method to construct cospectral graphs for the normalized Laplacian by a local modification in some graphs with special structure. Namely, under some simple assumptions, w…
The minimum rank problem over finite fields
Jason Grout
The structure of all graphs having minimum rank at most k over a finite field with q elements is characterized for any possible k and q. A strong connection between this characteri…
Program for calculating bounds on the minimum rank of a graph using Sage
Laura DeLoss, Jason Grout, Tracy McKay +2
The minimum rank of a simple graph is defined to be the smallest possible rank over all symmetric real matrices whose th entry (for ) is nonzero whenever …
Zero forcing for inertia sets
Steve Butler, Jason Grout, H. Tracy Hall
Zero forcing is a combinatorial game played on a graph with a goal of turning all of the vertices of the graph black while having to use as few "unforced" moves as possible. This l…
Table of minimum ranks of graphs of order at most 7 and selected optimal matrices
Laura DeLoss, Jason Grout, Leslie Hogben +3
The minimum rank of a simple graph is defined to be the smallest possible rank over all symmetric real matrices whose th entry (for ) is nonzero whenever …
The minimum rank problem over the finite field of order 2: minimum rank 3
Wayne Barrett, Jason Grout, Raphael Loewy
Our main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also l…