@article {
author = {Damadi, Hamid and Rahmati, Farhad},
title = {On matrix and lattice ideals of digraphs},
journal = {Transactions on Combinatorics},
volume = {7},
number = {2},
pages = {35-46},
year = {2018},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2017.105701.1510},
abstract = {Let $\textit{G}$ be a simple, oriented connected graph with $n$ vertices and $m$ edges. Let $I(\textbf{B})$ be the binomial ideal associated to the incidence matrix \textbf{B} of the graph $G$. Assume that $I_L$ is the lattice ideal associated to the rows of the matrix $\textbf{B}$. Also let $\textbf{B}_i$ be a submatrix of $\textbf{B}$ after removing the $i$-th row. We introduce a graph theoretical criterion for $G$ which is a sufficient and necessary condition for $I(\textbf{B})=I(\textbf{B}_i)$ and $I(\textbf{B}_i)=I_L$. After that we introduce another graph theoretical criterion for $G$ which is a sufficient and necessary condition for $I(\textbf{B})=I_L$. It is shown that the heights of $I(\textbf{B})$ and $I(\textbf{B}_i)$ are equal to $n-1$ and the dimensions of $I(\textbf{B})$ and $I(\textbf{B}_i)$ are equal to $m-n+1$; then $I(\textbf{B}_i)$ is a complete intersection ideal.},
keywords = {Directed graph,Binomial ideal,Matrix ideals},
url = {https://toc.ui.ac.ir/article_22320.html},
eprint = {https://toc.ui.ac.ir/article_22320_b7155094bae6e4bfec0b32c67a2295ec.pdf}
}