Research

Publications:

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

2. 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.

3. 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.

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

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

6. 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.

7. 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.

8.  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.

9.  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.

10. 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. E. Curl, S. Fallat, R. Moruzzi, C. Reinhart, D. Young. The zero forcing number of graph complements. http://arxiv.org/abs/2206.03932.

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

3. 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 Research Presentations:

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

• "Graphs with non-trivial Jordan blocks for the non-backtracking matrix", (in special session) Joint Mathematics Meetings, to be held in 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.

• "The normalized distance Laplacian", Faculty Seminar, Williams College, Williamstown, MA, November 22, 2019.

• "Cop throttling number: Bounds, values, and variants'', (in special session) AMS Sectional Meeting, Madison, Wisconsin, September 2019.

• "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.