37 citations · 69 across the 13 of their papers we have counts for
21 papers
Distinguishing graphs by their spectra, Smith normal forms and complements
Aida Abiad, Carlos A. Alfaro, Ralihe R. Villagrán
The search for a highly discriminating and easily computable invariant to distinguish graphs remains a challenging research topic. Here we focus on cospectral graphs whose compleme…
The degree-distance and transmission-adjacency matrices
Carlos A. Alfaro, Octavio Zapata
Let be a connected graph with adjacency matrix . The distance matrix of has rows and columns indexed by with -entry equal to the distance $\mathrm{d…
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…
Enumeration of cospectral and coinvariant graphs
Aida Abiad, Carlos A. Alfaro
We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (a cospectral mate), or at lea…
The structure of sandpile groups of outerplanar graphs
Carlos A. Alfaro, Ralihe R. Villagrán
We compute the sandpile groups of families of planar graphs having a common weak dual by evaluating the indeterminates of the critical ideals of the weak dual at the lengths of the…
Graphs with few trivial characteristic ideals
Carlos A. Alfaro, Michael D. Barrus, John Sinkovic +1
We give a characterization of the graphs with at most three trivial characteristic ideals. This implies the complete characterization of the regular graphs whose critical groups ha…
Eigenvalues, Smith normal form and determinantal ideals
Aida Abiad, Carlos A. Alfaro, Kristin Heysse +1
Determinantal ideals of graphs generalize, among others, the spectrum and the Smith normal form (SNF) of integer matrices associated to graphs. In this work we investigate the rela…
On transversal and 2-packing numbers in uniform linear systems
Carlos A. Alfaro, G. Araujo-Pardo, C. Rubio-Montiel +1
A linear system is a pair where is a family of subsets on a ground finite set , such that , for every $l,l^\prime \in \ma…
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…
On graphs with 2 trivial distance ideals
Carlos A. Alfaro
Distance ideals generalize the Smith normal form of the distance matrix of a graph. The family of graphs with 2 trivial distance ideals contains the family of graphs whose distance…
Critical ideals, minimum rank and zero forcing number
Carlos A. Alfaro, Jephian C. -H. Lin
There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is…
On a problem of Henning and Yeo about the transversal number of uniform linear systems whose 2-packing number is fixed
Carlos A. Alfaro, Adrián Vázquez-Ávila
A linear system is a pair where is a family of subsets on a ground finite set such that , for every $l,l^\prime \in \mat…
Distance ideals of graphs
Carlos A. Alfaro, Libby Taylor
We introduce the concept of distance ideals of graphs, which can be regarded as a generalization of the Smith normal form and the spectra of the distance matrix of a graph. We obta…
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…
On two-quotient strong starters for
Carlos A. Alfaro, Christian Rubio-Montiel, Adrián Vázquez-Ávila
Let be a finite additive abelian group of odd order , and let be the set of non-zero elements. A starter for is a set $S=\{\{x_i,y_i\}:i=1,\ldots,\…
The crossing number of the cone of a graph
Carlos A. Alfaro, Alan Arroyo, Marek Derunár +1
Motivated by a problem asked by Richter and by the long standing Harary-Hill conjecture, we study the relation between the crossing number of a graph and the crossing number of…
Critical ideals of signed graphs with twin vertices
Carlos A. Alfaro, Hugo Corrales, Carlos E. Valencia
This paper studies critical ideals of graphs with twin vertices, which are vertices with the same neighbors. A pair of such vertices are called replicated if they are adjacent, and…
Small clique number graphs with three trivial critical ideals
Carlos A. Alfaro, Carlos E. Valencia
The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. In this article we provide a set of minimal forbidden graphs…
Graphs with two trivial critical ideals
Carlos A. Alfaro, Carlos E. Valencia
The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. A basic property of the critical ideals of graphs asserts tha…
Dimension Reduction in Principal Component Analysis for Trees
Carlos A. Alfaro, Burcu Aydın, Elizabeth Bullitt +2
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed f…
On the Sandpile group of the cone of a graph
Carlos A. Alfaro, Carlos E. Valencia
In this article, we give a partial description of the sandpile group of the cone of the cartesian product of graphs in function of the sandpile group of the cone of their factors.…