In general, the value of the maximum nullity depends in the field. The most common case of is commonly assumed unless otherwise stated, in whihc case
is simply omitted from the notation.
AIM Minimum Rank--Special Graphs Work Group. "Zero Forcing Sets and the Minimum Rank of Graphs." Lin. Alg. Appl.428,
1628-1648, 2008.Almodovar, E.; DeLoss, L.; Hogben, L.; Hogenson, K.;
Murphy, K.; Peters, T.; and Ramírez, C. A. "Minimum Rank, Maximum Nullity
and Zero Forcing Number for Selected Graph Families." Involve: A Journal
of Mathematics3, 371-392, 2010.American Institute of Mathematics.
"Graph Catalog: Families of Graphs." https://aimath.org/WWN/matrixspectrum/catalog2.html.American
Institute of Mathematics. "AIM Minimum Rank Graph Catalog." http://admin.aimath.org/resources/graph-invariants/minimumrankoffamilies/#/super.American
Institute of Mathematics. "AIM Minimum Rank Graph Catalog References."
https://web.archive.org/web/20160207084159/http://orion.math.iastate.edu/lhogben/AIMmrgraphcatrefs.pdf.Barrett,
W.; Hunnell, M.; Hutchens, J.; and Sinkovic, J. "The Classification of Graphs
on 8 vertices with Coinciding Zero Forcing number and Maximum Nullity." 12 Jun
2025. https://arxiv.org/abs/2506.10726.Barrett,
W.; van der Holst, H.; and Loewy, R. "Graphs Whose Minimal Rank is Two."
Elec. J. Lin. Alg.11, 258-280, 2004.DeLoss, L.; Grout,
J.; Hogben, L.; McKay, T.; Smith, J.; and Tims, J. "Table of Minimum Ranks of
Graphs of Order at Most 7 and Selected Optimal Matrices." 4 Dec 2008. https://arxiv.org/abs/0812.0870.Fallat,
S. M. and Hogben, L. "Minimum Rank, Maximum Nullity, and Zero Forcing Number
of Graphs." Ch. 46 in Handbook of Linear Algebra, 2nd ed. Boca Raton,
FL: CRC Press, 2014.Nylen, P. M. "Minimum-Rank Matrices With
Prescribed Graph." Lin. Alg. Appl.248, 303-316, 1996.
be a field, 
be a simple undirected
graph on 
vertices, and let 
be the set of all 
symmetric matrices whose nonzero off-diagonal elements
occur in exactly the positions corresponding to the edges of 
. Then the maximum nullity 
is the maximum of the nullity
over all matrices in 
.
. The most common case of 
is commonly assumed unless otherwise stated, in whihc case
is simply omitted from the notation.
by the rank-nullity theorem
