论文标题
Posets的零局部图和与代数结构相关的图形的应用的颜色
Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures
论文作者
论文摘要
在本文中，我们表征了有限posets的弦和完美的零局部图。同样，事实证明，有限posets的零分量图以及有限$ 0 $ 0 $分配的posets的零局部图的补充满足了总体着色猜想。这些结果应用于有限的还原环的零分量图，comagimal Inder戒指的理想图，歼灭的理想图，环形理想的相交图以及循环基团子组的相交图。实际上，证明可以通过$ r $的特殊构造的poset的零局部图有效地研究了与通勤环$ r $与身份有效研究的这些图形。
In this paper, we characterize chordal and perfect zero-divisor graphs of finite posets. Also, it is proved that the zero-divisor graphs of finite posets and the complement of zero-divisor graphs of finite $0$-distributive posets satisfy the Total Coloring Conjecture. These results are applied to the zero-divisor graphs of finite reduced rings, the comaximal ideal graph of rings, the annihilating ideal graphs, the intersection graphs of ideals of rings, and the intersection graphs of subgroups of cyclic groups. In fact, it is proved that these graphs associated with a commutative ring $R$ with identity can be effectively studied via the zero-divisor graph of a specially constructed poset from $R$.
