Radio Number Associated with Zero Divisor Graph
نویسندگان
چکیده
منابع مشابه
THE ZERO-DIVISOR GRAPH OF A MODULE
Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, sayΓ(RM), such that when M=R, Γ(RM) coincide with the zero-divisor graph of R. Many well-known results by D.F. Anderson and P.S. Livingston have been generalized for Γ(RM). We Will show that Γ(RM) is connected withdiam Γ(RM)≤ 3 and if Γ(RM) contains a cycle, then Γ(RM)≤4. We will also show tha...
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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 کاملThe Zero-divisor Graph Associated to a Semigroup
The zero-divisor graph of a commutative semigroup with zero is the graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices adjacent if the product of the corresponding elements is zero. New criteria to identify zerodivisor graphs are derived using both graph-theoretic and algebraic methods. We find the lowest bound on the number of edges necessary to guar...
متن کاملthe zero-divisor graph of a module
let $r$ be a commutative ring with identity and $m$ an $r$-module. in this paper, we associate a graph to $m$, say ${gamma}({}_{r}m)$, such that when $m=r$, ${gamma}({}_{r}m)$ coincide with the zero-divisor graph of $r$. many well-known results by d.f. anderson and p.s. livingston have been generalized for ${gamma}({}_{r}m)$. we show that ${gamma}({}_{r}m)$ is connected with ${diam}({gamma}({}_...
متن کاملA module theoretic approach to zero-divisor graph with respect to (first) dual
Let $M$ be an $R$-module and $0 neq fin M^*={rm Hom}(M,R)$. We associate an undirected graph $gf$ to $M$ in which non-zero elements $x$ and $y$ of $M$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. Weobserve that over a commutative ring $R$, $gf$ is connected anddiam$(gf)leq 3$. Moreover, if $Gamma (M)$ contains a cycle,then $mbox{gr}(gf)leq 4$. Furthermore if $|gf|geq 1$, then$gf$ is finit...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2020
ISSN: 2227-7390
DOI: 10.3390/math8122187