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publications
The Characterization of Graphs Whose Sandpile Group has Fixed Number of Generators
Published in Extended Abstracts EuroComb 2021. Trends in Mathematics, 2021
Joint work with: C. A. Alfaro, M. D. Barrus and J. Sinkovic
Recommended citation: Carlos A. Alfaro, Michael D. Barrus, John Sinkovic and Ralihe R. Villagrán. (2021) "The Characterization of Graphs Whose Sandpile Group has Fixed Number of Generators" Extended Abstracts EuroComb 2021. Trends in Mathematics, vol 14. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-83823-2_91
Graphs with few trivial characteristic ideals
Published in Linear Algebra and its Applications, 2021
Joint work with: C. A. Alfaro, M. D. Barrus and J. Sinkovic
Recommended citation: Carlos A. Alfaro, Michael D. Barrus, John Sinkovic, Ralihe R. Villagrán. "Graphs with few trivial characteristic ideals." Linear Algebra and its Applications. 615, (2021), Pages 155-174. https://doi.org/10.1016/j.laa.2020.12.024
The structure of sandpile groups of outerplanar graphs
Published in Applied Mathematics and Computation, 2021
Joint work with: Carlos A. Alfaro
Recommended citation: Carlos A. Alfaro and Ralihe R. Villagrán . " The structure of sandpile groups of outerplanar graphs." Applied Mathematics and Computation. 395 (2021), 125861. https://doi.org/10.1016/j.amc.2020.125861
Algorithmic aspects of arithmetical structures
Published in Linear Algebra and its Applications, 2022
Joint work with: Carlos E. Valencia
Recommended citation: Carlos E. Valencia and Ralihe R. Villagrán. " Algorithmic aspects of arithmetical structures." Linear Algebra and its Applications. 640 (2022), Pages 191-208. https://doi.org/10.1016/j.laa.2022.01.020
Constructions of cospectral graphs with different zero forcing numbers
Published in Electronic Journal of Linear Algebra, 2022
Joint work with: A. Abiad, B. Brimkov, J. Breen, T. R. Cameron and H. Gupta
Recommended citation: A. Abiad, B. Brimkov, J. Breen, T. R. Cameron, H. Gupta and R. R. Villagrán. "Constructions of cospectral graphs with different zero forcing numbers." Electronic Journal of Linear Algebra. 38 (2022), pp. 280-294. https://doi.org/10.13001/ela.2022.6737
Hadamard Diagonalizable Graphs of Order at Most 36
Published in The Electronic Journal of Combinatorics, 2022
Joint work with: Jane Breen, Steve Butler, Melissa Fuentes, Bernard Lidický, Michael Phillips, Alexander W. N. Riasanovsky, Sung-Yell Song, Cedar Wiseman and Xiaohong Zhang
Recommended citation: Jane Breen, Steve Butler, Melissa Fuentes, Bernard Lidický, Michael Phillips, Alexander W. N. Riasanovsky, Sung-Yell Song, Ralihe R. Villagrán, Cedar Wiseman and Xiaohong Zhang. "Hadamard Diagonalizable Graphs of Order at Most 36." The Electronic Journal of Combinatorics. 29(2), P2.16 (2022). https://doi.org/10.37236/9725
Distinguishing graphs with two integer matrices
Published in ArXiV, 2023
Joint work with: C. A. Alfaro and Octavio Zapata
Recommended citation: Carlos A. Alfaro, Ralihe R. Villagrán and Octavio Zapata. "Distinguishing graphs with two integer matrices." arXiv:2309.15365. (2023) https://doi.org/10.48550/arXiv.2309.15365
Arithmetical structures on dominated polynomials
Published in São Paulo Journal of Mathematical Sciences, 2023
Joint work with: Carlos E. Valencia
Recommended citation: Carlos E. Valencia Ralihe R. Villagrán. "Arithmetical structures on dominated polynomials." São Paulo Journal of Mathematical Sciences. 17, (2023), pages 430-439. https://doi.org/10.1007/s40863-022-00336-6
The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions
Published in Graphs and Combinatorics, 2024
Joint work with: S. Allred, E. Curl, S. Fallat, S. Nasserasr, H. Schuerger and P. K. Vishwakarma
Recommended citation: S. Allred, E. Curl, S. Fallat, S. Nasserasr, H. Schuerger, R. R. Villagrán and P. K. Vishwakarma. "The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions." Graphs and Combinatorics. 40, 20 (2024). https://doi.org/10.1007/s00373-023-02745-6
Evolutive sandpiles
Published in Physica A: Statistical Mechanics and its Applications, 2025
Joint work with: Carlos A. Alfaro, Juan Pablo Serrano and Ralihe R. Villagrán
Recommended citation: Carlos A. Alfaro, Juan Pablo Serrano and Ralihe R. Villagrán. "Evolutive sandpiles." Physica A: Statistical Mechanics and its Applications. 657, (2025), 130248. https://doi.org/10.1016/j.physa.2024.130248
Distinguishing graphs by their spectra, Smith normal forms and complements
Published in Applied Mathematics and Computation, 2025
Joint work with: Aida Abiad and Carlos A. Alfaro
Recommended citation: Aida Abiad, Carlos A. Alfaro and Ralihe R. Villagrán. "Distinguishing graphs by their spectra, Smith normal forms and complements." Applied Mathematics and Computation. 490, (2025), 129198. https://doi.org/10.1016/j.amc.2024.129198
The Characterization of Graphs with Two Trivial Distance Ideals
Published in ArXiV, 2025
Joint work with: C. A. Alfaro, Teresa I. Hoekstra-Mendoza and Juan Pablo Serrano
Recommended citation: Carlos A. Alfaro, Teresa I. Hoekstra-Mendoza, Juan Pablo Serrano and Ralihe R. Villagrán. "The Characterization of Graphs with Two Trivial Distance Ideals." arXiv:2504.11706. (2025) https://doi.org/10.48550/arXiv.2504.11706
Determinantal ideals of graphs
Published in Handbook of Visual, Experimental and Computational Mathematics, 2025
Joint work with: C. A. Alfaro and J. P. Serrano
Recommended citation: Carlos A. Alfaro, Juan P. Serrano and Ralihe R. Villagrán. (2025) "Determinantal ideals of graphs." Handbook of Visual, Experimental and Computational Mathematics, Springer, Cham, (2025) https://doi.org/10.1007/978-3-030-83823-2_91
Distance ideals of digraphs
Published in Applied Mathematics and Computation, 2025
Joint work with: Carlos A. Alfaro, Teresa I. Hoekstra-Mendoza and Juan Pablo Serrano
Recommended citation: Carlos A. Alfaro, Teresa I. Hoekstra-Mendoza, Juan Pablo Serrano and Ralihe R. Villagrán. "Distance ideals of digraphs." Applied Mathematics and Computation. 500, (2025), 129430. https://doi.org/10.1016/j.amc.2025.129430
Graphs with two trivial distance ideals over the polynomial ring with integer coefficients
Published in International Symposium on Symbolic and Algebraic Computation (2025) (ISSAC 2025), 2025
Joint work with: C. A. Alfaro, T. I. Hoekstra-Mendoza and J. P. Serrano
Recommended citation: C. A. Alfaro, T. I. Hoekstra-Mendoza, J. P. Serranoc and Ralihe R. Villagrán. (2025) "Graphs with two trivial distance ideals over the polynomial ring with integer coefficients." in International Symposium on Symbolic and Algebraic Computation (2025) (ISSAC 2025)., ACM, New York, NY, USA. https://doi.org/10.1145/3747199.3747577
Skirting the n-tuples
Published in ArXiV, 2026
Joint work with: Sam Adriaensen, Ferdinand Ihringer and William J. Martin
Recommended citation: Sam Adriaensen, Ferdinand Ihringer, William J. Martin and Ralihe R. Villagrán. "Skirting the n-tuples." arXiv:2602.01080. (2026) https://doi.org/10.48550/arXiv.2602.01080
talks
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Conference Proceeding talk 3 on Relevant Topic in Your Field
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teaching
Previous Courses
Prev course, , 2025
Calculus IV (group 5)
Undergraduate course, Worcester Polytechnic Institute, Department of Mathematical Sciences, 2026
Course description:
This course provides an introduction to multivariable calculus. Topics covered include: vector functions, partial derivatives and gradient, multivariable optimization, double and triple integrals, polar coordinates, other coordinate systems and applications.