32 citations · 49 across the 4 of their papers we have counts for
7 papers
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…
Arithmetical structures on graphs with connectivity one
Hugo Corrales, Carlos E. Valencia
Given a graph , an arithmetical structure on is a pair of positive integer vectors such that and \[ (\mathrm{…
Arithmetical structures on graphs
Hugo Corrales, Carlos E. Valencia
Arithmetical structures on a graph were introduced by Lorenzini as some intersection matrices that arise in the study of degenerating curves in algebraic geometry. In this article…
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…
Critical ideals of trees
Hugo Corrales, Carlos E. Valencia
Given a graph , its generalized Laplacian matrix is given by \[ L(G,X_G)_{u,v}= \begin{cases} x_u&\text{if }u=v,\\ -m_{uv}&\text{if }u\neq v, \end{cases} \] where $X_G=\{…
On the critical ideals of graphs
Hugo Corrales, Carlos E. Valencia
We introduce some determinantal ideals of the generalized Laplacian matrix associated to a digraph G, that we call critical ideals of G. Critical ideals generalize the critical gro…