论文标题
在通勤环的必需歼灭 - 理想图中着色
Coloring in essential annihilating-ideal graphs of commutative rings
论文作者
论文摘要
通勤性环$ r $的基本灭绝 - 理想图$ \ MATHCAL {在本文中，我们表明$ \ Mathcal {eg}（r）$是弱完美的，如果$ r $是noetherian的，并且给出了$ \ mathcal {eg}（r）$的集团数量的明确公式。此外，所有基本歼灭 - 理想图的结构都具有$ 2 $的颜色数量。除其他结果外，还检查了$ \ mathcal {eg}（r）$的双重组数和边缘色数。
The essential annihilating-ideal graph $\mathcal{EG}(R)$ of a commutative unital ring $R$ is a simple graph whose vertices are non-zero ideals of $R$ with non-zero annihilator and there exists an edge between two distinct vertices $I,J$ if and only if $Ann(IJ)$ has a non-zero intersection with any non-zero ideal of $R$. In this paper, we show that $\mathcal{EG}(R)$ is weakly perfect, if $R$ is Noetherian and an explicit formula for the clique number of $\mathcal{EG}(R)$ is given. Moreover, the structures of all rings whose essential annihilating-ideal graphs have chromatic number $2$ are fully determined. Among other results, twin-free clique number and edge chromatic number of $\mathcal{EG}(R)$ are examined.
