Research

Publications:

1. K. Heysse, K. Lorenzen, C. Reinhart. Defective eigenvalues of the non-backtracking matrix. To appear in Electron. J. Linear Algebra.

2. B. Bjorkman, C. Bozeman, D. Ferrero, M. Flagg, C. Grood, L. Hogben, B. Jacob, C. Reinhart. Power domination reconfiguration. To appear in La Matematica.

3. E. Curl, S. Fallat, R. Moruzzi, C. Reinhart, D. Young. On the zero forcing number of the complement of graphs with forbidden subgraphs. Linear Algebra Appl. 703 (2024), 187-207. 

4. L. Hogben, C. Reinhart. Variants of distance matrices of graphs and digraphs: a survey.  La Matematica (2022).

5. J. Carlson, R. Eagleton, J. Geneson, J. Petrucci, C. Reinhart, P. Sen. The damage throttling number of a graph. Australas. J. Comb. 80 (2021), 361-385.

6. A. Bonato, J. Breen, B. Brimkov, J. Carlson, S. English, J. Geneson, L. Hogben, K.E. Perry, C. Reinhart. Cop throttling number: Bounds, values, and variants. To appear in Journal of Combinatorics.  https://arxiv.org/abs/1903.10087.

7. C. Reinhart. The normalized distance Laplacian. Special Matrices. 9 (2021), 1-18. Supporting documents.

8. M. Catral, L. Ciardo, L. Hogben, C. Reinhart. Spectral theory of products of digraphs. Elect. Journal of Linear Alg. 36 (2020), 44-763.

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

10. K. Boyer, B. Birmkov, S. English, D. Ferrero, A. Keller, R. Kirsch, M. Phillips, C. Reinhart. The zero forcing polynomial of a graph. Discrete Appl. Math. 258 (2019), 35-48.

11.  J. Breen, B. Brimkov, J. Carlson, L. Hogben, K.E. Perry, C. Reinhart. Throttling for the game of Cops and Robbers on graphs. Discrete Math. 341 (2018), 2418-2430.

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

13. C. Bozeman, M. Catral, B. Cook, O. E. González, C. Reinhart. On the tree cover number of a graph. Involve 10 (2017), 767-779.

Publications under review:

1. B. Bjorkman, L. Cao, F. Kenter, R. Moruzzi, C. Reinhart, V. Vasilevska. Leaky Forcing: Extending Zero Forcing Results to a Fault-Tolerant Setting. https://arxiv.org/abs/2508.02564. 

2. E. Curl, J. Kritschgau, C. Reinhart, H. van der Holst. The inverse eigenvalue problem for probe graphs. https://arxiv.org/abs/2402.18670.

3. J. Carlson, M. Halloran, C. Reinhart. The multi-robber damage number of a graph. http://arxiv.org/abs/2205.06956.

4. B. Bjorkman, C. Bozeman, D. Ferrero, M. Flagg, C. Grood, L. Hogben, B. Jacob, C. Reinhart. Power domination reconfiguration. https://arxiv.org/abs/2201.01798.

Selected Invited Conference Presentations:

• "Defective eigenvalues for the non-backtracking matrix'', (in minisymposium) Canadian Discrete and Algorithmic Mathematics Conference, Ottawa, Canada, May 22nd, 2025.

• "The inverse eigenvalue problem for probe graphs", (in special session) Joint Mathematics Meetings, San Francisco, California, January, 2024.

• "Graphs with non-trivial Jordan blocks for the non-backtracking matrix", (in special session) Joint Mathematics Meetings, San Francisco, California, January, 2024.

• "The zero forcing number of graph complements", (in special session) 54th Southeastern Conference on Graph Theory Combinatorics and Computing, Boca Raton, Florida, March, 2023.

• "The zero forcing number of graph complements", (in special session) Joint Mathematics Meetings, Boston, Massachusetts, January 5, 2023.

• "The distance matrix and its variants for digraphs'' (in mini-symposium) 23rd International Linear Algebra Society (ILAS) Conference, Galway, Ireland, June 23, 2022.

• "Distance cospectral constructions of digraphs", (in minisymposium) 2021 SIAM Conference on Applied Linear Algebra, held virtually in May, 2021.

• "The damage throttling number of a graph", (in special session) Joint Mathematics Meetings, held virtually, January 7th, 2021.

• "Product throttling for the game of Cops and Robbers'', (in special session) 51st Southeastern Conference on Graph Theory Combinatorics and Computing, Boca Raton, Florida, March 9th, 2020.

• "The normalized distance Laplacian'', (in special session) Joint Mathematics Meetings, in Denver, CO, January 16, 2020.

• "Throttling for the game of Cops and Robbers",  (in mini-symposium) 22nd International Linear Algebra Society (ILAS) Conference, Rio de Janeiro, Brazil, July 9th, 2019.

• "The normalized distance Laplacian", (in special session) 50th Southeastern Conference on Graph Theory Combinatorics and Computing, Boca Raton, Florida, March 8, 2019.

• "Applications of SMP to the determination of the minimum number of distinct eigenvalues," (in MAA Enhancing Diversity in Graduate Education (EDGE) session) Joint Mathematics Meetings, San Diego, CA, January 11, 2018.

• "Results on the minimum number of distinct eigenvalues of graphs", (in mini-symposium) 21st International Linear Algebra Society (ILAS) Conference, Ames, IA, July 28, 2017.

Selected Invited Seminars and Colloquia:

• "Misbehaving matrices: Defective eigenvalues for the non-backtracking matrix'', Department of Mathematics Colloquium,  Purdue University, October 28, 2025.

• "The game of Cops and Robbers on graphs", DREAMS Colloquium, Villanova University, May 13, 2024. 

• "The game of Cops and Robbers on graphs", Bi-Co Math Colloquium, Haverford College, March 18, 2024.

• "The nonbacktracking matrix", Algebraic Graph Theory Seminar, Organized  virtually by the University of Waterloo, January 15, 2024.

• "The nonbacktracking matrix", Department of Mathematics, Discrete Math and Algebra Seminar, University of Delaware, November 17, 2023.

• "The game of Cops and Robbers on graphs", Department of Mathematics, Combinatorics, Algebra, and Topology Seminar, United States Naval Academy, October 28, 2022.

• "The distance matrix and its variants for graphs and digraphs", Department of Mathematics and Statistics Colloquium, Villanova University, October 7, 2021.

• "The game of Cops and Robbers", Department of Mathematics Colloquium, California State University, East Bay, held virtually, September 17, 2021.

• "The normalized distance Laplacian", Class of 1960s Speaker, Department of Mathematics and Statistics Faculty Seminar, Williams College, Williamstown, MA, November 22, 2019.