相关论文: On the intersection graph of ideals of $\mathbb{Z}…

Let $R$ be a commutative ring with identity and $\Bbb A (R)$ be the set of ideals of $R$ with non-zero annihilator. The annihilator-ideal graph of $R$, denoted by $A_{I} (R) $, is a simple graph with the vertex set $\Bbb A(R)^{\ast} := \Bbb…

Let $G$ be a finite simple connected graph on $[n]$ and $R = K[x_1, \ldots, x_n]$ the polynomial ring in $n$ variables over a field $K$. The edge ideal of $G$ is the ideal $I(G)$ of $R$ which is generated by those monomials $x_ix_j$ for…

Let P = k[x_1, ..., x_n] be the polynomial ring in n variables. A homogeneous ideal I of P generated in degree d is called Gotzmann if it has the smallest possible Hilbert function out of all homogeneous ideals with the same dimension in…

A set of edges $\Gamma$ of a graph $G$ is an edge dominating set if every edge of $G$ intersects at least one edge of $\Gamma$, and the edge domination number $\gamma_e(G)$ is the smallest size of an edge dominating set. Expanding on work…

Let $G$ be a finite simple graph, and $J_G$ denote the binomial edge ideal of $G$. In this article, we first compute the $\mathrm{v}$-number of binomial edge ideals corresponding to Cohen-Macaulay closed graphs. As a consequence, we obtain…

This paper introduces a new approach to associating a graph with a commutative ring. Let $R$ be a commutative ring with identity. The unit-zero divisor graph of a commutative ring $R$, denoted by $G_{UZ}(R)$, offers a novel framework for…

Let $G$ be a finite group and $N(G)$ be the set of its conjugacy class sizes excluding~$1$. Let us define a directed graph $\Gamma(G)$, the set of vertices of this graph is $N(G)$ and the vertices $x$ and $y$ are connected by a directed…

Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $r$ be a positive integer. We consider the hypergraph $\mathrm{Con}_r(G)$ whose vertices are the vertices of $G$ and the (hyper)edges are all $A\subseteq V(G)$ such that…

Assume that $G$ is a finite group. For every $a, b \in\mathbb N,$ we define a graph $\Gamma_{a,b}(G)$ whose vertices correspond to the elements of $G^a\cup G^b$ and in which two tuples $(x_1,\dots,x_a)$ and $(y_1,\dots,y_b)$ are adjacent if…

Let $G$ be a finite simple graph on $n$ non-isolated vertices, and let $J_G$ be its binomial edge ideal. We determine almost all pairs $(\text{projdim}(J_G),\text{reg}(J_G))$, where $G$ ranges over all finite simple graphs on $n$…

Let A_1,...,A_k be a collection of families of subsets of an n-element set. We say that this collection is cross-intersecting if for any i,j in [k] with i not equal to j, A in A_i and B in A_j implies that the intersection of A and B is…

Let $G$ be a finite simple graph on the vertex set $V(G) = \{x_{1}, \ldots, x_{n}\}$ and match$(G)$, min-match$(G)$ and ind-match$(G)$ the matching number, minimum matching number and induced matching number of $G$, respectively. Let…

A set D of vertices of a graph G=(V,E) is irredundant if each v of D satisfies (a) v is isolated in the subgraph induced by D, or (b) v is adjacent to a vertex in V-D that is nonadjacent to all other vertices in D. The upper irredundance…

A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…

An intersection graph of curves in the plane is called a string graph. Matousek almost completely settled a conjecture of the authors by showing that every string graph of m edges admits a vertex separator of size O(\sqrt{m}\log m). In the…

The {\em independent domination number} $\gamma^i(G)$ of a graph $G$ is the maximum, over all independent sets $I$, of the minimal number of vertices needed to dominate $I$. It is known \cite{abz} that in chordal graphs $\gamma^i$ is equal…

Let M be a module over a commutative ring R. In this paper, we continue our study of annihilating-submodule graph AG(M) which was introduced in (The Zariski topology-graph of modules over commutative rings, Comm. Algebra., 42 (2014),…

Given a set $\mathcal{F}$ of graphs, we call a copy of a graph in $\mathcal{F}$ an $\mathcal{F}$-graph. The $\mathcal{F}$-isolation number of a graph $G$, denoted by $\iota(G,\mathcal{F})$, is the size of a smallest set $D$ of vertices of…

Let $G=(V,E)$ be a graph and $n$ a positive integer. Let $I_n(G)$ be the abstract simplicial complex whose simplices are the subsets of $V$ that do not contain an independent set of size $n$ in $G$. We study the collapsibility numbers of…

Let $R$ be a commutative ring with unity. The prime ideal sum graph of the ring $R$ is a simple undirected graph whose vertex set is the set of nonzero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if…