Distance ideals of digraphs
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.
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Short CV
Education
- Ph.D in Mathematics, Department of Mathematics, Center for Research and Advanced Studies of the National Polytechnic Intitute (CINVESTAV-IPN), 2021
- M.S. in Mathematics, Department of Mathematics, Center for Research and Advanced Studies of the National Polytechnic Intitute (CINVESTAV-IPN), 2017.
- B.S. in Mathematics, Faculty of Physics and Mathematics, Autonomous University of Sinaloa, Mexico, 2014
Publications
Journal publications
Distinguishing graphs by their spectra, Smith normal forms and complements
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.
Evolutive sandpiles
Carlos A. Alfaro, Juan Pablo Serrano and Ralihe R. Villagrán. "Evolutive sandpiles." Physica A: Statistical Mechanics and its Applications. 657, (2025), 130248.
The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions
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).
Arithmetical structures on dominated polynomials
Carlos E. Valencia Ralihe R. Villagrán. "Arithmetical structures on dominated polynomials." São Paulo Journal of Mathematical Sciences. 17, (2023), pages 430-439.
Hadamard Diagonalizable Graphs of Order at Most 36
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).
Constructions of cospectral graphs with different zero forcing numbers
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.
Algorithmic aspects of arithmetical structures
Carlos E. Valencia and Ralihe R. Villagrán. " Algorithmic aspects of arithmetical structures." Linear Algebra and its Applications. 640 (2022), Pages 191-208.
The structure of sandpile groups of outerplanar graphs
Carlos A. Alfaro and Ralihe R. Villagrán . " The structure of sandpile groups of outerplanar graphs." Applied Mathematics and Computation. 395 (2021), 125861.
Graphs with few trivial characteristic ideals
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.
Refereed conference
Graphs with two trivial distance ideals over the polynomial ring with integer coefficients
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.
Determinantal ideals of graphs
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)
The Characterization of Graphs Whose Sandpile Group has Fixed Number of Generators
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.
Submitted
Skirting the n-tuples
Sam Adriaensen, Ferdinand Ihringer, William J. Martin and Ralihe R. Villagrán. "Skirting the n-tuples." arXiv:2602.01080. (2026)
The Characterization of Graphs with Two Trivial Distance Ideals
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)
Distinguishing graphs with two integer matrices
Carlos A. Alfaro, Ralihe R. Villagrán and Octavio Zapata. "Distinguishing graphs with two integer matrices." arXiv:2309.15365. (2023)
Teaching
Work experience
- Postdoctotal Scholar, August 2023 - current position
- Mathematical Sciences Department, Worcester Polytechnic Institute (WPI)
- Research Mentor: Bill Martin
- Postdoctoral Researcher, June 2022 -May 2023
- Department of Mathematics and Computer Science, Eindhoven University of Technology (TU/e)
- Mentor: Aida Abiad