Research Papers etc.


Leslie Hogben
Professor, Department of Mathematics, and Associate Dean, College of Liberal Arts and Sciences, Iowa State University
Associate Director for Diversity, American Institute of Mathematics



This page is outdated. See ArXiv for recent papers.

The primary emphasis of my current research is in linear algebra, combinatorics, and applications of linear algebra to other fields.  A long time ago I worked in ring theory (Jordan and other nonassociative algebras and connections between ring theory and universal algebra).



Papers on minimum rank/maximum nullity/Colin De Verdiere parameters/zero forcing/power domination/propagation time/throttling of a graph or sign pattern.

Catalog of graphs listing minimum rank


Product throttling
S.E. Anderson, K.L. Collins, D. Ferrero, L. Hogben, C. Mayer, A.N. Trenk, S. Walker. In Recent Trends in Graph Theory and Applications, Springer, 2021. [arxiv]

Product throttling for power domination
S.E. Anderson, K.L. Collins, D. Ferrero, L. Hogben, C. Mayer, A.N. Trenk, S. Walker.  [arxiv]

Reconfiguration graphs of zero forcing sets
J. Geneson, R. Haas, L. Hogben.  [arxiv]

Skew throttling

E. Curl, J. Geneson, L. Hogben.  Australasian J . Combinatorics, 78 (2020), 117-190. [arxiv]

Using Markov chains to determine expected propagation time for probabilistic zero forcing.
Y. Chan, E. Curl, J. Geneson, L. Hogben, K. Liu, I. Odegard, M.S. Ross. Electronic J. Linear Algebra 36 (2020) 318-333

Cop throttling number: Bounds, values, and variants.
A. Bonato, J. Breen, B. Brimkov, J. Carlson, S. English, J. Geneson, L. Hogben, K.E. Perry.  To appear in  J. Comb.[arXiv]

Propagation time for probabilistic zero forcing
J. Geneson, L. Hogben.  [arXiv]

Rigid linkages and partial zero forcing
D. Ferrero, M. Flagg, H.T. Hall, L. Hogben, J.C.-H. Lin, S.A. Meyer, S. Nasserasr, B. Shader. Electron. J. Combinatorics, 26 (2019) P2.43

Throttling for the game of Cops and Robbers  on graphs

J. Breen, B. Brimkov, J. Carlson, L. Hogben, K.E. Perry, C. Reinhart. Discrete Math., 341 (2018) 2418–2430.
[arXiv]

Restricted power domination and zero forcing problems 
C. Bozeman, B. Brimkov, C. Erickson, D. Ferrero, M. Flagg, L. Hogben. J. Combinatorial Optimization, 37 (2019), 935–956. [arXiv]

Families of graphs with maximum nullity equal to zero forcing number
J.S. Alameda, E. Curl, A. Grez, L. Hogben, O'N. Kingston, A. Schulte, D. Young, M. Young. Special Matrices 6 (2018), 56 - 67 [PDF in ISU DR]

Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph
B. Bjorkman, L. Hogben, S. Ponce, C. Reinhart, T. Tranel.  Pure Appl. Funct. Anal. 3 (2018), 537--563. [arXiv]

Throttling positive semidefinite zero forcing propagation time on graphs
J. Carlson, L. Hogben, J. Kritschgau, K. Lorenzen, M.S. Ross, S. Selken, V. Valle Martinez. Discrete Appl. Math. 254 (2019), 33–46. [arXiv]

The inverse eigenvalue problem of a graph: Multiplicities and minors
W. Barrett, S Butler, S.M. Fallat, H.T. Hall, L Hogben, J.C.-H. Lin, B.L. Shader, M. Young.
[arXiv]

The relationship between k-forcing and k-power domination.
  
D. Ferraro, L. Hogben, F.H.J. Kenter, M. Young. Discrete Math. 341 (2018), 1789–1797. [arXiv]


Note on Nordhaus-Gaddum problems for power domination 
K.F. Benson, D. Ferrero, M. Flagg, V. Furst, L. Hogben, V. Vasilevska. 
Discrete Appl. Math.,  251 (2018),  103--113. [arXiv]

Multi-part Nordhaus-Gaddum type problems for tree-width, Colin de Verdi\`ere type parameters, and Hadwiger number.   
L. Hogben, J.C.-H. Lin, M. Young. 
[arXiv]

Note on power propagation time and lower bounds for power domination number 
D. Ferraro, L. Hogben, F.H.J. Kenter, M. Young.   J. Combinatorial Optimization, 34 (2017), 736-641.  [arXiv]

Generalizations of the Strong Arnold Property and  the minimum number of distinct eigenvalues of  a graph 
W. Barrett, S. Fallat, H. T. Hall,  L. Hogben, J. C.-H. Lin, B.L. Shader Electron. J. Combinatorics, 24 (2017) P2.40 (28 pages).


Zero forcing and power domination for graph products
 
K.F. Benson, D. Ferrero, M. Flagg, V. Furst, L. Hogben, V. Vasilevska, B. Wissman.   Australasian J. Combinatorics 70 (2018), 221-235.  [arXiv]


Fractional Zero Forcing via Three-color Forcing Games 
L. Hogben, K. Palmowski, D. Roberson, M. Young.  Discrete Appl. Math., 213 (2016),  114-129.  [arXiv]

Orthogonal representations, projective rank, and fractional minimum positive semidefinite rank: connections and new directions 
L. Hogben,  K. Palmowski, D. E. Roberson, S. Severini. Electronic J. Linear Algebra 32 (2017), 98-115.

Zero forcing propagation time on oriented graphs 
A. Berliner, C. Bozeman, S. Butler, M. Catral, L. Hogben, B. Kroschel, J.C.-H. Lin, N. Warnberg, M. Young.   Discrete Appl. Math. 224 (2017), 45-59.
[PDF in ISU DR]

Nordhaus-Gaddum Problems for Colin de Verdiere Type Parameters, Variants of Tree-width, and Related Parameters 
L. Hogben. 
Recent Trends in Combinatorics, IMA Volume in Mathematics and its Applications, Springer, 2016. [PDF in ISU DR]

Minimum rank of graphs with loops
C. Bozeman, AV. Ellsworth, L. Hogben, J.C.-H. Lin, G. Maurer, K. Nowak, A. Rodriguez, J. Strickland.
Electron. J. Linear Algebra  27 (2014):  907 – 934. 

Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs
A. Berliner, C. Brown, J. Carlson, N. Cox, L. Hogben, J. Hu, K. Jacobs, K. Manternach, T. Peters, N. Warnberg, M. Young
 Involve 8 (2015): 147 – 167. [PDF in ISU DR]

Minimum rank with zero diagonal
C. Grood, J. Harmse, L. Hogben, T.J. Hunter, B. Jacob, A. Klimas, S. McCathern
Electronic Journal of Linear Algebra, 27 (2014), pp. 458-477.

The maximum nullity of a complete subdivision graph is equal to its zero forcing number 
W. Barrett, S, Butler,
M. Catral, S. Fallat, H.T. Hall, L. Hogben, M. Young   Electronic Journal of Linear Algebra, 27 (2014), 444-457.

Minimum rank, maximum nullity, and zero forcing number for simple digraphs
A. Berliner, M. Catral, L. Hogben, M. Huynh, K. Lied, M. Young.
 
Electronic Journal of Linear Algebra, 26 (2013), 762-780.

Note on Nordhaus-Gaddum problems for Colin de Verdiere type parameters 
W. Barrett, S. Fallat, H. T. Hall, L. Hogben. Electronic Journal of Combinatorics, 20 (2013) P56 (9 pages).

Zero forcing number, maximum nullity, and path cover number of subdivided graphs
 
M. Catral, A. Cepek, L. Hogben, M. Huynh, Kirill Lazebnik, Travis Peters, Michael Young Electronic Journal of Linear Algebra, 23 (2012), 906-922.

Propagation time for zero forcing on a graph
L. Hogben, M. Huynh, S. Meyer, N. Kingsley, S. Walker, M. Young.  Discrete Applied Mathematics 160 (2012) 1994-2005.

Positive semidefinite zero forcing number  
J. Ekstrand, C. Erickson,  H.T. Hall, D. Hay, R. Johnson, N. Kingsley, S. Osborne, T. Peters, J. Roat, A. Ross, D. Row, N. Warnberg, M. Young).   
Linear Algebra and its Applications, 439 (2013): 1862 – 1874.


Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees
J. Ekstrand, C. Erickson, D. Hay, L. Hogben, J. Roat. Electonic Journal of Linear Algebra 23 (2012) 79-87.


On the Graph Complement Conjecture for minimum rank
F.
Barioli, W. Barrett, S. Fallat, H.T. Hall,  L. Hogben, H. van der Holst Linear Algebra and its Applications. 436 (2012): 4373–4391.

Minimum rank of certain families of graphs
E. Almodovar, L. DeLoss, L. Hgben, K. Hogenson, K. Murphy, T. Peters, C. Ramirez.  Involve: a journal of mathematics 3 (2010): 371-392. [PDF in ISU DR]

Parameters related to tree-width, zero forcing, and maximum nullity of a graphs
F. Barioli, W. Barrett, S. Fallat, H.T. Hall,  L. Hogben, B. Shader, P. van den Driessche, H.
van der Holst. Journal of Graph Theory 72 (2013), 146 – 177 [PDF in ISU DR]

Vertex and edge spread of zero forcing number, maximum nullity, and 
minimum rank of a graph
C.
Edholm, L. Hogben, M. Huynh, J, LaGrange, D. Row. Linear Algebra and its Applications 436 (2012): 4352–4372.

A note on minimum rank and maximum nullity of  sign patterns
L. Hogben Electron. J. Linear Algebra 22 (2011) 203-213.


Zero forcing parameters and minimum rank problems
F. Barioli, W. Barrett, S. Fallat, H.T. Hall,  L. Hogben, B. Shader, P. van den Driessche, H.
van der Holst. Linear Algebra and its Applications 433 (2010) 401–411.

Expected values of parameters associated with the minimum rank of a graph
H.T.
Hall, L. Hogben, R. Martin, B. Shader. Linear Algebra and its Applications 433 (2010) 101–117.

Techniques for determining the minimum rank of a small graph
L. DeLoss, J. Grout, L. Hogben, T. McKay, J. mith, G. Tims.
  Linear Algebra and its Applications 432 (2010) 2995–3001.

Minimum rank of skew-symmetric matrices described by a graph
IMA-ISU research group on minimum rank (16 authors) 
Linear Algebra and its Applications 432 (2010) 2457–2472.

Minimum rank problems
L. Hogben. Linear Algebra and its Applications 432 (2010) 1961–1974
.

Generic maximum nullity of a graph

L. Hogben, B. Shader.
Linear Algebra and its Applications 432 (2010) 857–866

Universally optimal matrices and field independence of the minimum rank of a graph (with DeAlba, Grout, Mikkelson, Rasmussen) Electronic Journal of Linear Algebra 18 (2009): 403-419.

On the minimum rank of not necessarily symmetric matrices: A preliminary study
F. Barioli, S.M. Fallat, H.T. Hall, D. Hershkowitz, L. Hogben, H. van der Holst, B. Shader.
  Electronic Journal of Linear Algebra 18 (2009): 126-145.

An upper bound for the minimum rank of a graph
A. Berman, S. Friedland, L. Hogben, U. Rothblum, B. Shader.
  Linear Algebra and its Applications 429/7 (2008) 1629 – 1638.

Orthogonal representations, minimum rank, and graph complements
L. Hogben, Linear Algebra and its Applications, 428/11-12 (2008) 2560-2568.


Zero forcing sets and the minimum rank  of graphs
AIM minimum rank - special graphs work group (18 authors) 
Linear Algebra and its Applications, 428/7 (2008) 1628–1648.

Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers
A. Berman, S. Friedland, L. Hogben, U. Rothblum, B. Shader.  Electronic Journal of Combinatorics, 15/1 (2008) R 25 (19 pages).  Appendix

The Minimum Rank of Symmetric Matrices Described by a Graph: A Survey
S. Fallat, L. Hogben.
  Linear Algebra and its Applications, 426 (2007) 558-582. [PDF]

Minimum Rank of a Tree over an Arbitrary Field
N.L. Chenette, S.V. Droms, L. Hogben, R. Mikkelson, O. Pryporova) 
  Electronic Journal of Linear Algebra 16 (2007): 183-186.

Forbidden Minors for the Class of Graphs G with xi(G) <= 2
L. Hogben, H. van der Holst. 
Linear Algebra and its Applications 423 (2007) 42-52. 

Rational Realization of Maximum Eigenvalue Multiplicity of Symmetric Tree Sign Patterns
A. Chowdhury, L. Hogben, J. Melancon, R. Mikkelson, 
Linear Algebra and its Applications 418 (2006) 380-393.

Minimum Rank and Maximum Eigenvalue Multiplicity of Symmetric Tree Sign Patterns
L.M. DeAlba, T. Hardy, I.R. Hentzel, L. Hogben, A. Wangsness), 
Linear Algebra and its Applications 418 (2006) 389-415.

A variant on the graph parameters of Colin de Verdiere: Implications to the minimum rank of graphs

F. Barioli, S.M. Fallat, L. Hogben.  
Electronic Journal of Linear Algebra 13 (2005), 387-404

Spectral Graph Theory and the Inverse Eigenvalue Problem of a Graph
L. Hogben. 
Electronic Journal of Linear Algebra 14 (2005): 12-31

On the Difference between Maximal Multiplicity and Path Cover Number for Tree-like Graphs
F. Barioli, S.M. Fallat, L. Hogben.   Linear Algebra and its Applications, 409 (2005) 13-31

Computation of Path Cover Number and Minimal Rank for Graphs  
F. Barioli, S.M. Fallat, L. Hogben.   Linear Algebra and its Applications 392 (2004):289-303.    

Papers on distance spectra and spectral graph theory

Spectra of variants of distance matrices of graphs and digraphs: a survey. To
L. Hogben, C. Reinhart. To appear in La Matematica. [arxiv]

Spectral theory of products of digraphs.
M. Catral, L. Ciardo, L. Hogben, C. Reinhart. Electronic J. Linear Algebra 36 (2020)744-763

Graphs that are cospectral for the distance Laplacian
B. Brimkov, K. Duna, L. Hogben, K. Lorenzen, C. Reinhart, S.-Y. Song, M. Yarrow.  Electronic J. Linear Algebra 36 (2020) 334-351

On the distance spectra of graphs
   
G. Aalipour, A. Abiad, Z. Berikkyzy, J. Cummings, J. De Silva, W. Gao, K. Heysse, L. Hogben, F.H.J. Kenter, J.C.-H. Lin, M. Tait.  Linear Algebra Appl., 497 (2016), 66-87. 
[arXiv]

Proof of a conjecture of Graham and Lovasz concerning unimodality of coefficients of the distance characteristic polynomial of a tree 
G. Aalipour, A. Abiad, Z. Berikkyzy, L. Hogben, F.H,J. Kenter, J.C.-H. Lin, M.Tait.
Electron. J. Linear Algebra 34 (2018) 373–380



Papers on eventually nonnegative matrices and their sign patterns

Note on the Jordan form of  an irreducible eventually nonnegative matrix
L. Hogben, B.-S. Tam, U. Wilson.  Note on the Jordan form of an irreducible eventually nonnegative matrix.  Electron. J. Linear Algebra, 30 (2015), 279-285.


Potentially eventually exponentially positive sign patterns
M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben, X. Martinez-Rivera, A. Ochoa.  Involve 6 (2013): 261-271.
  [PDF in ISU DR]

Eventual properties of matrices
L. Hogben and U. Wilson.
Electronic Journal of Linear Algebra, 23 (2012), 953-965.

Sign patterns that allow strong eventual nonnegativity
M. Catral, C. Erickson, L. Hogben, D. Olesky, P. van den Driessche.
Electronic Journal of Linear Algebra 23 (2012): 1-10.

Constructions of potentially eventually positive sign patterns with reducible positive part
M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben, X. Martinez-Rivera, A. Ochoa.  Involve 4 (2011): 405-410   [PDF in ISU DR]

Eventually cyclic matrices and a test for strong eventual nonnegativity
L. Hogben.
Electronic Journal of Linear Algebra 19 (2010): 129-140.

Sign patterns that require or allow power-positivity
M. Catral, L.Hogben, D. Olesky, P. van den Driessche.
Electronic Journal of Linear Algebra 19 (2010): 121-128

Sign patterns that allow eventual positivity
A. Berman, M. Catral, L.M. DeAlba, A. Elhashash, F. Hall, L. Hogben, I.-J. Kim, D. Olesky, P. Tarazaga, M. Tsatsomeros, P. van den Driessche.
Electronic Journal of Linear Algebra  19 (2010): 108-120.

Sign patterns that require eventual positivity or require eventual nonnegativity
E. Ellison, L. Hogben, M. Tsatsomeros.
Electronic Journal of Linear Algebra 19 (2010): 98-107.

Papers on positivity and matrix completion problems

SPN graphs. 
L. Hogben, N. Shaked-Monderer. Electronic Journal of Linear Algebra 35 (2019): 376-386.

The Q-Matrix Completion Problem
L.M. DeAlba, L. Hogben, B.K.Sarma. 
Electronic Journal of Linear Algebra 18 (2009): 176-191. 

The Copositive Matrix Completion Problem: Unspecified Diagonal
L. Hogben. Linear Algebra and its Applications  420 (2007) 160-162.   

On completion problems for various classes of P-matrices 

Bowers, Evers, Shaner, Snider, Wangsness) 
Linear Algebra and its Applications   413 (2006) 342-354.

The Copositive Matrix Completion Problem
L.Hogben, C.R. Johnson,R. Reams.   Linear Algebra and its Applications
408 (2005) 207-211

Relationships between the Completion Problems for Various Classes of Matrices
Proceedings of the 2003 SIAM Conference on Applied Linear Algebra   [ PDF ]

The (Weakly) Sign Symmetric P-Matrix Completion Problems
L.M. DeAlba, T. Hardy, L. Hogben, A. Wangsness.
  Electronic Journal of Linear Algebra 10 (2003): 257-271 

The Nonnegative P0 -Matrix Completion Problem
J.Y. Choi, L.M. DeAlba, L. Hogben, B. Kivunge, S. Nordstrom, M. Shedenhelm.
Electronic Journal of Linear Algebra 10 (2003): 46-59 

Matrix Completion Problems for Pairs of Related Classes of Matrices
L. Hogben. Linear Algebra and its Applications 373 (2003): 13-29  

The P0-Matrix Completion Problem
J.Y. Choi, L.M. DeAlba, L. Hogben, M. Maxwell, A. Wangsness
Electronic Journal of Linear Algebra 9 (2002): 1-20 

The Symmetric M-Matrix and Symmetric Inverse M-Matrix Completion Problems
 L. Hogben. Linear Algebra and its Applications 353 (2002): 159-167   

Graph Theoretic Methods for Matrix Completion Problems
L. Hogben. Linear Algebra and its Applications 328 (2001): 161-202  

Completions of P-Matrix Patterns
Luz DeAlba, Leslie Hogben
Linear Algebra and its Applications 319 (2000): 83-102  

Inverse M-Matrix Completions of Patterns Omitting Some Diagonal Positions
L. Hogben. Linear Algebra and its Applications 313 (2000): 173-192

Completions of Inverse M-Matrix Patterns
L. Hogben. Linear Algebra and its Applications 282 (1998): 145-160.  

Completions of M-Matrix Patterns
L. Hogben. Linear Algebra and its Applications 285 (1998): 143-152.

Papers on principal rank characteristic sequences

The sepr-sets of sign patterns.
L. Hogben, J.C.-H. Lin, D. D. Olesky, P. van den Driessche. Linear Multilinear Algebra. ,.8 (2020),  2044-2068. [arXiv]

The enhanced principal rank characteristic sequence for Hermitian matrices. 

S. Butler, M. Catral, H.T. Hall, L. Hogben, X. Martinez-Rivera, B. Shader, And P. van den Driessche. The enhanced principal rank characteristic sequence for Hermitian matrices. Electronic J Linear Algebra 32 (2017), 58-75.


The enhanced principal rank characteristic sequence.
 
S. Butler,
M. Catral, S. Fallat, T. Hall, L. Hogben, P. van den Driessche, M. YoungLinear Algebra and its Applications 498 (2016) 181-200 [PDF in ISU DR]

The principal rank characteristic sequence over various fields. 
W. Barrett, S. Butler,
M. Catral, S. Fallat, T. Hall, L. Hogben, P. van den Driessche, M. Young  Linear Algebra and its Applications 459 (2014), 222–236.

Papers on applications of linear algebra and graph theory

Note on von Neumann and Renyi entropies of a Graph
M. Dairyko, L. Hogben, J.C.-H. Lin, J. Lockhart, D. Roberson, S. Severini, M. Young. Linear Algebra Appl.  521 (2017), 240-253 [arXiv]

Logic circuits from zero forcing
D
. Burgarth, V. Giovanetti, L. Hogben, S. Severini, M. Young. 
Natural Computing 14 (2015), 485–490.  [arXiv]

Zero forcing, linear and quantum controllability for systems evolving on networks. 
D. Burgarth, D. D'Alessandro, L. Hogben, S. Severini, M. Young.   IEEE Transactions on Automatic Control
58 (2013): 2349 – 2354 [arXiv

Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise
C. Qui, N. Vaswani, B. Lois, L. Hogben.  IEEE Transactions on Information Theory, 60 (2014): 5007 – 5039.   [arXiv
- the material in this link is copyright 2014 by IEEE]

Papers on crossing numbers

Crossing numbers of complete tripartite and balanced complete multipartite graphs. 
Ellen Gethner, Leslie Hogben,
Bernard Lidicky, Florian Pfender, Amanda Ruiz, Michael YoungJ Graph Theory 84 (2017) 552–565 [arXiv]

Papers on rainbow arithmethic progressions

Rainbow arithmetic progressions.  Steve Butler, Craig Erickson, Leslie Hogben, Kirsten Hogenson, Lucas Kramer, Richard L. Kramer, Jephian Chin-Hung Lin, Ryan R. Martin, Derrick Stolee, Nathan Warnberg, Michael Young. J Combintorics 7 (2016), 595-626 [arXiv]

Papers on Partition Regular matrices

A linear algebraic view of partition regular matrices
L. Hogben, J. McLeod
.    Linear Algebra and its Applications 433 (2010) 1809–1820 

Papers on Spectrally Arbitrary sign/nonzero Patterns

Spectrally Arbitrary Patterns: Reducibility and the 2n Conjecture
L.M. DeAlba,  I.R. Hentzel, L. Hogben, J.J. McDonald, R. Mikkelson, O. Pryporova, B. Shader, K. Vander Meulen.
Linear Algebra and Its Applications, 423 (2007)  262-276.

Papers on Stable and Convergent Matrices

Multiplicative Perturbations of Stable and Convergent Operators,
Bryan Cain, Luz M. DeAlba, Leslie Hogben, Charles R. Johnson
Linear Algebra and Its Applications 268 (1998): 151-169.


Slides from some recent plenary talks



 
Leslie Hogben's Homepage 2021