in this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. weobserve that over a commutative ring $r$, $bbb{ag}_*(_rm)$ isconnected and diam$bbb{ag}_*(_rm)leq 3$. moreover, if $bbb{ag}_*(_rm)$ contains a cycle, then $mbox{gr}bbb{ag}_*(_rm)leq 4$. also for an $r$-module $m$ with$bbb{a}_*(m)neq s(m)setminus {0}$, $...

‎for any group $g$‎, ‎we define an equivalence relation $thicksim$ as below‎: ‎[forall g‎, ‎h in g gthicksim h longleftrightarrow |g|=|h|]‎ ‎the set of sizes of equivalence classes with respect to this relation is called the same-order type of $g$ and denote by $alpha{(g)}$‎. ‎in this paper‎, ‎we give a partial answer to a conjecture raised by shen‎. ‎in fact‎, ‎we show that if $g$ is a nilpote...

In this paper, we consider transformations for posets with the same upper bound graph. Those $poset_{8}$ can be $tran8formed$ into each other by a finite sequence of two kinds of transformations, called addition and deletion of an order relation. This result induces a characterization on unique upper bound graphs. We deal with the distance of those posets that have the same upper bound graph. I...

 Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors.  The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero  zero-divisors of  $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

introduction: noise is one of the hazardous factors in work places such as  textile industries. the objective of this study is to determine noise pollution in textile industries in kermanshah (2001). materials & methods: this study is  an analytical-descriptive one. the study was done in 2 steps. in the first step the characteristics of the work place & buildings were completely determined; the...

The aim of the study was to determine whether or not delivery of live music poses a significant risk to the hearing of musicians involved and to evaluate current practices that are employed (if any) to protect the hearing of musicians. Method: consisted of two parts; firstly monitoring of noise exposure levels at four gigs with the application of dose meters, and secondly the completion of a qu...