37 citations · 126 across the 16 of their papers we have counts for
20 papers
Arithmetical structures on dominated polynomials
Carlos E. Valencia, Ralihe R. Villagrán
In~\cite{algorithmic} was given an algorithm that computes arithmetical structures on matrices. We use some of the ideas contained there to get an algorithm that computes arithmeti…
Algorithmic aspects of arithmetical structures
Carlos E. Valencia, R. R. Villagrán
Arithmetical structures on graphs were first introduced in \cite{Lorenzini89}. Later in \cite{arithmetical} they were further studied in the setting of square non-negative integer…
Computing sandpile configurations using integer linear programming
Carlos A. Alfaro, Carlos E. Valencia, Marcos C. Vargas
It is well known that recurrent sandpile configurations can be characterized as the optimal solution of certain optimization problems. In this article, we present two new integer l…
The equivalence between two classic algorithms for the assignment problem
Carlos A. Alfaro, Sergio L. Perez, Carlos E. Valencia +1
We give a detailed review of two algorithms that solve the minimization case of the assignment problem. The Bertsekas' auction algorithm and the Goldberg & Kennedy algorithm. We wi…
Digraphs with at most one trivial critical ideal
Carlos A. Alfaro, Carlos E. Valencia, Adrián Vázquez-Ávila
Critical ideals generalize the critical group, Smith group and the characteristic polynomials of the adjacency and Laplacian matrices of a graph. We give a complete characterizatio…
Counting Arithmetical Structures on Paths and Cycles
Benjamin Braun, Hugo Corrales, Scott Corry +6
Let be a finite, simple, connected graph. An arithmetical structure on is a pair of positive integer vectors such that $(\mathrm{diag}(\mathbf{d})-A…