let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

We present a generalization of the so-called σ-game, introduced by Sutner [9], a combinatorial game played on a graph, with relations to cellular automata, as well as odd domination in graphs. A configuration on a graph is an assignment of values in {0, . . . , p− 1} (where p is an arbitrary positive integer) to all the vertices of G. One may think of a vertex v of G as a button the player can ...

We describe Green’s relations on the partition monoid, two of its submonoids, and the related Jones and Brauer monoids. Key Words: partition monoid, Jones monoid, ideal structure 2000 Mathematics Subject Classi…cation: 20M20 1 The partition monoid and some submonoids The elements of the partition monoid Pn [5, 8, 9] are equivalence classes of graphs on a vertex set n [ n0 = f1; 2; :::ng [ f10; ...

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

Abstract To each colored graph one can associate its closure in the universal space of isomorphism classes pointed graphs, and this subspace be regarded as a generalized subshift. Based on correspondence, we introduce two definitions for chaotic (colored) them analogous to Devaney’s. We show equivalence our novel chaos, proving their topological genericity various subsets space.

In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].  

‎In this paper, first we introduce the end of locally finite graphs as an equivalence class of infinite paths in the graph. Then we mention the ends of finitely generated groups using the Cayley graph. It was proved that the number of ends of groups are not depended on the Cayley graph and that the number of ends in the groups is equal to zero, one, two, or infinity. For ...

Aspect-Oriented Programming (AOP) is an emerging technology whose goal is to modularize concerns that may involve several classes. The purpose of this report is to describe how one of the main representatives of AOP, namely Hyper/J, was used to implement a simple yet illustrative product-line of graph algorithms. 1 The Graph Product Line (GPL) The Graph Product-Line (GPL) [5] is a family of cla...