Related papers: Zero-Divisor Graphs and Zero-Divisor Functors

In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In [2] and [3] the authors generalized…

We determine the automorphism group of the zero-divisor digraph of the semiring of matrices over an antinegative commutative semiring with a finite number of zero-divisors.

We compute generators and relations for the section ring of a rational divisor on an elliptic curve. Our technique generalizes the work of O'Dorney (in genus zero) and Voight--Zureick-Brown (for specific divisors arising from the study of…

Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of mathematics, including number theory, finite algebra,…

We define the graph minor category and prove that the category of contravariant representations of the graph minor category over a Noetherian ring is locally Noetherian. This can be regarded as a categorification of the Robertson--Seymour…

In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…

Let R be a commutative ring with a non-zero identity. In this paper, we define a new graph, the compressed intersection annihilator graph, denoted by $IA(R)$, and investigate some of its theoretical properties and its relation with the…

We revisit a classical paper about (even hole, triangle)-free graphs [Conforti, Cornu\'ejols, Kapoor and Vu\v skovi\'c, Triangle-free graphs that are signable without even holes, Journal of Graph Theory, 34(3), 204--220, 2000]. In fact, the…

In this paper, we introduce a graph structure, called non-zero component graph on finite dimensional vector spaces. We show that the graph is connected and find its domination number and independence number. We also study the…

In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…

Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is independent set of $G$, if no two vertices of $S$ are adjacent. The independence number $\alpha(G)$ is the size of a maximum independent set in the graph. %An independent set with…

We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Gr\"obner theory. We give an explicit description of a minimal Gr\"obner bases for each higher syzygy module. In each…

Let $G$ be a $p$-group. We begin to consider the relationship between the structure of the commuting graph and $|G:Z(G)|$. We also build a family of groups whose commuting graphs have more than one connected component whose diameter is at…

In this paper we study some of the basic properties of a graph which is constructed from the equivalence classes of non-zero zero-divisors determined by annihilator ideals of a poset. In particular, we demonstrate how this graph helps in…

Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$, denoted by $\Gamma'(R)$, is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of $R$, and two distinct vertices $x$ and $y$ are…

An approach to identify the normal subgroups determined by ideals in free group rings with the help of the derived functors of non-additive functors is explored. A similar approach, i.e., via derived functors, for computing limits of…

The proper divisor graph $\Upsilon_n$ of a positive integer $n$ is the simple graph whose vertices are the proper divisors of $n$, and in which two distinct vertices $u, v$ are adjacent if and only if $n$ divides $uv$. The graph…

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…

This paper defines, for each graph $G$, a flag vector $fG$. The flag vectors of the graphs on $n$ vertices span a space whose dimension is $p(n)$, the number of partitions on $n$. The analogy with convex polytopes indicates that the linear…

Let R be a commutative ring with identity and let J be an ideal of R. In this paper, we introduce and investigate the notion of the i-extended ideal-based cozero-divisor graph of R. This graph, denoted by $\overline{\Gamma''}_{Ji}(R)$, is a…