The zero-divisor graph with respect to ideals of a commutative semiring
نویسندگان
چکیده
منابع مشابه
The Zero-divisor Graph with Respect to Ideals of a Commutative Semiring
In a manner analogous to a commutative ring, the idealbased zero-divisor graph of a commutative semiring R can be defined as the undirected graph ΓI(R) for some ideal I of R. The properties and possible structures of the graph ΓI (R) are studied.
متن کاملThe total graph of a commutative semiring with respect to proper ideals
Let $I$ be a proper ideal of a commutative semiring $R$ and let $P(I)$ be the set of all elements of $R$ that are not prime to $I$. In this paper, we investigate the total graph of $R$ with respect to $I$, denoted by $T(Gamma_{I} (R))$. It is the (undirected) graph with elements of $R$ as vertices, and for distinct $x, y in R$, the vertices $x$ and $y$ are adjacent if and only if $x + y in P(I)...
متن کاملAn Ideal-based Zero-divisor Graph of a Commutative Semiring
There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate the interplay between the semiring-theoretic properties of R and the graph-theoretic properties of ΓI(R) for some ideal I of R. We also show tha...
متن کاملthe total graph of a commutative semiring with respect to proper ideals
let $i$ be a proper ideal of a commutative semiring $r$ and let $p(i)$ be the set of all elements of $r$ that are not prime to $i$. in this paper, we investigate the total graph of $r$ with respect to $i$, denoted by $t(gamma_{i} (r))$. it is the (undirected) graph with elements of $r$ as vertices, and for distinct $x, y in r$, the vertices $x$ and $y$ are adjacent if and only if $x + y in p(i)...
متن کاملMedian and Center of Zero-Divisor Graph of Commutative Semigroups
For a commutative semigroup S with 0, the zero-divisor graph of S denoted by &Gamma(S) is the graph whose vertices are nonzero zero-divisor of S, and two vertices x, y are adjacent in case xy = 0 in S. In this paper we study median and center of this graph. Also we show that if Ass(S) has more than two elements, then the girth of &Gamma(S) is three.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasnik Matematicki
سال: 2008
ISSN: 0017-095X
DOI: 10.3336/gm.43.2.06