Dio Lewis Holl Chair in Applied Mathematics and Professor, Department of Mathematics, Iowa State University

Associate Director for Diversity, American Institute of Mathematics

- Papers: Minimum rank/maximum nullity/zero forcing number/Colin de Verdiere number of a graph or pattern
- Papers: Spectral Graph Theory
- Papers: Sign Patterns and Eventually nonnegative matrices
- Papers: Applications of linear algebra and combinatorics

- Papers: Principal rank characteristic sequences
- Papers: Matrix Completion Problems (combinatorial)
- Papers: Crossing numbers

- Papers: Rainbow arithmetic progressions

- Papers: Partition Regular Matrices

- Papers: Spectrally Arbitrary Sign/nonzero Patterns
- Papers: Stable and Convergent Matrices
- Selected Slides from Talks
- Handbook of Linear Algebra

- Linear Algebra Sites

I am the Dio Lewis Holl Chair in Applied Mathematics at Iowa State University mad the Associate Director for Diversity of the American Institute of Mathematics.

I am the Secretary/Treasurer of the International Linear Algebra Society.

I am the editor of Handbook of Linear Algebra and an editor of Recent Trends in Combinatorics.

I am an associate editor of Linear Algebra and its Applications and an associate editor of Electronic Journal of Linear Algebra.

There is an active ISU Discrete Mathematics Research Cluster that operates the Discrete Mathematics Seminar meeting weekly during the academic year and graduate students are encouraged to attend. I frequently lead the ISU Combinatorial Matrix Theory Research Group, sometimes as an REU (research experiences for undergraduates) or EGR (early graduate research) group.

Catalog of graphs listing minimum rank

Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph

Beth Bjorkman, Leslie Hogben, Scarlitte Ponce, Carolyn Reinhart, Theodore Tranel. [PDF preprint]

Throttling positive semidefinite zero forcing propagation time on graphs

J. Carlson, L. Hogben, J. Kritschgau, K. Lorenzen, M.S. Ross, V. Valle Martinez. [PDF preprint]

The inverse eigenvalue problem of a graph: Multiplicities and minors

Wayne Barrett, Steve Butler, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Jephian C.-H. Lin, Bryan L. Shader, Michael Young. [PDF preprint]

The relationship between k-forcing and k-power domination. D. Ferraro, L. Hogben, F.H.J. Kenter, M. Young. [PDF preprint]

Note on Nordhaus-Gaddum problems for power domination

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. [PDF Preprint]

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. [PDF Preprint]

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). [link to PDF]

Power domination

Fractional Zero Forcing via Three-color Forcing Games

Orthogonal representations, projective rank, and fractional minimum positive semidefinite rank: connections and new directions

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 preprint]

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

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. [PDF]

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]

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, Volume 27, pp. 458-477 [PDF]

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. [PDF]

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 [PDF]

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). [PDF]

Zero forcing number, maximum nullity, and path cover number of subdivided graphs. Minerva Catral, Anna Cepek, Leslie Hogben, My Huynh, Kirill Lazebnik, Travis Peters, Michael Young. Electronic Journal of Linear Algebra, 23 (2012), 906-922 [PDF]

Propagation time for zero forcing on a graph. Leslie Hogben, My Huynh, Sarah Meyer, Nicole Kingsley, Shanise Walker, Michael Young. Discrete Applied Mathematics 160 (2012) 1994-2005. [PDF]

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. [PDF ]

Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees. (with Ekstrand, Erickson, Hay, Roat). Electonic Journal of Linear Algebra 23 (2012) 79-87 [PDF]

On the Graph Complement Conjecture for minimum rank (with Barioli, Barrett, Fallat, Hall,
van der Holst) Linear Algebra and its Applications. 436 (2012): 4373–4391 [PDF]

Minimum rank of certain families of graphs

(with Almodovar, DeLoss, Hogenson, Murphy, Peters, Ramirez) Involve: a journal of mathematics 3 (2010): 371-392. [PDF]

*
*

minimum rank of a graph

Generic maximum nullity of a graph

On the minimum rank of not necessarily symmetric matrices: A preliminary study

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

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

**On the Difference between
Maximal
Multiplicity and Path Cover Number for Tree-like Graphs **(with
Barioli and Fallat) *Linear Algebra and its
Applications, *409 (2005)
13-31[PDF
]

**Computation of Path Cover
Number
and Minimal Rank for Graphs **(with
Barioli and Fallat)
*Linear Algebra and its Applications*** 392**
(2004):289-303.
[PDF ]

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. [PDF preprint]

The enhanced principal rank characteristic sequence. S. Butler, M. Catral, S. Fallat, T. Hall, L. Hogben, P. van den Driessche, M. Young.

The principal rank characteristic sequence over various fields. Wayne Barrett, S. Butler, M. Catral, S. Fallat, T. Hall, L. Hogben, P. van den Driessche, M. Young.

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

Zero forcing, linear and quantum controllability for systems evolving on networks. Daniel Burgarth, Domenico D'Alessandro, Leslie Hogben, Simone Severini, Michael Young. IEEE Transactions on Automatic Control 58 (2013): 2349 – 2354 [PDF preprint - this material in this link is copyright 2013 by IEEE]

On completion problems for various classes of P-matrices

**The Copositive Matrix
Completion
Problem **(with Johnson and
Reams)
*Linear Algebra and its Applications* **408**
(2005) 207-211 [PDF
preprint ]

**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** (with
DeAlba, Hardy, Wangsness)

*Electronic
Journal of Linear Algebra*** 10** (2003): 257-271

**The Nonnegative P _{0}
-Matrix Completion Problem** ( with Choi, DeAlba, Kivunge,
Nordstrom,
Shedenhelm)

**Matrix Completion Problems
for
Pairs of Related Classes of Matrices**

*Linear
Algebra and its Applications***
373**
(2003): 13-29
[ PDF preprint ]

**The P _{0}-Matrix
Completion
Problem** ( with Choi, DeAlba, Maxwell, Wangsness)

**The Symmetric M-Matrix and
Symmetric
Inverse M-Matrix Completion Problems**

*Linear Algebra
and its Applications* **353** (2002):
159-167 [
PDF preprint ]

**Graph Theoretic Methods for
Matrix
Completion Problems**

*Linear
Algebra and its Applications ***328*** *(2001):
161-202 [PDF preprint
]

**Completions of P-Matrix
Patterns**
(with Luz DeAlba)

* Linear
Algebra and its Applications ***319** (2000): 83-102
[
PDF preprint ]

**Inverse M-Matrix
Completions
of Patterns Omitting Some Diagonal Positions**

*
Linear Algebra and its Applications* **313** (2000):
173-192.

**Completions of Inverse
M-Matrix
Patterns**

*Linear Algebra and its Applications
***282**
(1998): 145-160.

**Completions of M-Matrix
Patterns**

*Linear Algebra and its Applications* **285**
(1998): 143-152.

- International Linear Algebra Society (ILAS)
- Electronic Journal of Linear Algebra (ELA)
- Linear Algebra and Its
Applications (LAA)
Editors
of LAA

- Linear
and Multilinear Algebra (LAMA)

- Minimum
Rank Graph Catalogs

- Spectral Graph Theory Homepage

- ISU Linear Algebra Seminar (old)
- ISU Discrete Math Seminar

- 15th ILAS Conference
Cancun

- Pictures
from China July 2007: 2nd ICAC (Beijing, Xi'an) and 14th ILAS
(Shanghai)

- AIM Workshop: Spectra of families of matrices described by graphs, digraphs, and sign patterns, Oct. 23-27, 2006
- Pictures
from AIM
Workshop

- Special Session on Combinatorial Matrix Theory, AMS Sectional Meeting, Lincoln, NE, Oct. 21-23, 2005
- Minisymposium: Spectral Properties of Families of Matrices described by Patterns or Graphs at 12th ILAS Conference, Regina, June 26-29, 2005
- 12th ILAS Conference, Regina, Canada, June 26-29, 2005
- Pictures from Directions In Combinatorial Matrix Theory Workshop, BIRS, Banff, Canada, May 6-8, 2004
- Topics in Linear Algebra Conference ISU, Ames. IA, September 13-14, 2002
- Pictures from
Combinatorial Matrix
Theory
Conference,
Pohang, Korea, January 14-17, 2002

Leslie Hogben's Homepage | Feb. 20, 2017 |