Results 51 to 60 of about 88,501 (223)

Component graphs of vector spaces and zero-divisor graphs of ordered sets

AKCE International Journal of Graphs and Combinatorics
In this paper, nonzero component graphs and nonzero component union graphs of finite-dimensional vector spaces are studied using the zero-divisor graph of a specially constructed 0–1-distributive lattice and the zero-divisor graph of rings.
Nilesh Khandekar, Peter J. Cameron, Vinayak Joshi   +2 more
doaj   +1 more source

The Zero Divisor Graph of the Ring Z_(2^2 p)

ARO-The Scientific Journal of Koya University, 2016
In this paper, we consider the crossing number and the chromatic number of the zero divisor graph Γ(Z_(2^2 p)) to show that this type of zero divisor graphs is bipartite graph, and the smallest cycle in Γ(Z_(2^2 p)) is of length four this implies that ...
Nazar H. Shuker, Payman A. Rashed
doaj   +1 more source

Generalized Irreducible Divisor Graphs [PDF]

, 2013
In 1988, I. Beck introduced the notion of a zero-divisor graph of a commutative rings with $1$. There have been several generalizations in recent years. In particular, in 2007 J. Coykendall and J. Maney developed the irreducible divisor graph.
Mooney, Christopher Park
core  

On bipartite zero-divisor graphs

Discrete Mathematics, 2009
AbstractA (finite or infinite) complete bipartite graph together with some end vertices all adjacent to a common vertex is called a complete bipartite graph with a horn. For any bipartite graph G, we show that G is the graph of a commutative semigroup with 0 if and only if it is one of the following graphs: star graph, two-star graph, complete ...
Tongsuo Wu, Dancheng Lu
openaire   +2 more sources

Strong External Difference Families and Classification of α $\alpha $‐Valuations

Journal of Combinatorial Designs, EarlyView.
ABSTRACT One method of constructing (a2+1,2,a,1) $({a}^{2}+1,2,a,1)$‐SEDFs (i.e., strong external difference families) in Za2+1 ${{\mathbb{Z}}}_{{a}^{2}+1}$ makes use of α $\alpha $‐valuations of complete bipartite graphs Ka,a ${K}_{a,a}$. We explore this approach and we provide a classification theorem which shows that all such α $\alpha $‐valuations ...
Donald L. Kreher, Maura B. Paterson, Douglas R. Stinson   +2 more
wiley   +1 more source

General infinitesimal variations of the Hodge structure of ample curves in surfaces

Mathematische Nachrichten, EarlyView.
Abstract Given a smooth projective complex curve inside a smooth projective surface, one can ask how its Hodge structure varies when the curve moves inside the surface. In this paper, we develop a general theory to study the infinitesimal version of this question in the case of ample curves.
Víctor González‐Alonso, Sara Torelli
wiley   +1 more source

Ring Classification of Ideal-Based Zero Divisor Graph with Vertices 9

Al-Kitab Journal for Pure Sciences
Let R be a finite commutative ring with a non-zero unit, and L be an ideal of R. focuses on expanding the notation of the Zero Divisor Graph to create what is known as the Ideal-Based Zero Divisor Graph. The main goal is to classify rings using the ideal-
Husam Q. Mohammad, Sahbaa A. Younus, Wafa Y. Yahya   +2 more
doaj   +1 more source

Commutative rings with ideal based zero divisor graph of orders 12,13 and 14 [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics
An recent years, several studies have emerged on the graphs for commutative rings. Researchers have investigated ideal based zero-divisor graphs linked to commutative rings, delving into the characteristics of these graphs.
Raad Shukur, Husam Mohammad
doaj   +1 more source

On some properties of the asymptotic Samuel function

Mathematische Nachrichten, EarlyView.
Abstract The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here, we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring.
A. Bravo, S. Encinas, J. Guillán‐Rial
wiley   +1 more source

A note on the zero divisor graph of a lattice [PDF]

Transactions on Combinatorics, 2014
Let $L$ be a lattice with the least element $0$. An element $xin L$ is a zero divisor if $xwedge y=0$ for some $yin L^*=Lsetminus left{0right}$. The set of all zero divisors is denoted by $Z(L)$.
T. Tamizh Chelvam , S. Nithya
doaj