For an arbitrary ring $R$, the zero-divisor graph of $R$, denoted by $Gamma (R)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $R$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. It is well-known that for any commutative ring $R$, $Gamma (R) cong Gamma (T(R))$ where $T(R)$ is the (total) quotient ring of $R$. In this...

We consider $2$-colourings $f : E(G) \rightarrow \{ -1 ,1 \}$ of the edges a graph $G$ with colours $-1$ and $1$ in $\mathbb{Z}$. A subgraph $H$ is said to be zero-sum under $f$ if $f(H) := \sum_{e\in E(H)} f(e) =0$. study following type questions, several cases obtaining best possible results: Under which conditions on $|f(G)|$ can we guarantee existence spanning tree $G$? The types are comple...

various authors have considered the zero-rest-mass equation and the contour integral representation of its solutions. ferber generalized these equations to supertwistor spaces with 2n odd components so that with n=o we get the standard ungraded twistors of penrose. in this paper we use the batchelor theorem toconstruct the natural super twistor space with coarse topology with underlying standar...

This study investigated the potential effects of egg quality indices at 95% confidence level in order to minimize quality loss during different storage conditions. The chicken and quail eggs’ quality indices including weight, albumen index, yolk index, Haugh index in fresh eggs as well as after storing in moist sawdust, oil, and refrigerator were measured for six weeks. The results revealed tha...