论文标题
l（2，1） - 与交换环相关的一些零径都的标签
L(2, 1)-labeling of some zero-divisor graphs associated with commutative rings
论文作者
论文摘要
令$ \ MATHCAL {G} =（\ Mathcal {V}，\ Mathcal {e}）$是一个简单的图表，$ l（2,1）$ - 标记$ \ Mathcal {g} $的标签是由$ \ Mathcal of Adj get factection from toge fectere fertice facect of toge fercal calcal calcal can} calcal的范围{距离距离二的两个，以及彼此之间的顶点有不同的标签。 $ \ Mathcal {G} $的$λ$ -NUMBER，由$λ（\ Mathcal {g}）$表示，是最小的正整数$ \ ell $，因此$ \ Mathcal {g} $具有$ L（2,1）$ - 与所有标签一样标记为$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \;有限的交换环$ r $与Unity的零划分图，由$γ（r）$表示，是一个简单的图形，其顶点的全部为零$ r $，其中两个顶点$ u $和$ v $在$ r $ in $ r $中的$ uv = 0 $时才邻接。在本文中，我们研究了$ L（2,1）$ - 一些零局部图的标签。我们研究了Partite截断，这是一种图形操作，使我们能够从明显更大的订单图中获得相对较小的订单的缩小图。我们建立了图形的$λ$数字及其部分截断之间的关系。我们利用操作的部分截断将还原环的零径向图收缩到布尔环的零径向图。
Let $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ be a simple graph, an $L(2,1)$-labeling of $\mathcal{G}$ is an assignment of labels from nonnegative integers to vertices of $\mathcal{G}$ such that adjacent vertices get labels which differ by at least by two, and vertices which are at distance two from each other get different labels. The $λ$-number of $\mathcal{G}$, denoted by $λ(\mathcal{G})$, is the smallest positive integer $\ell$ such that $\mathcal{G}$ has an $L(2,1)$-labeling with all labels as members of the set $\{0,1, \dots,\ell\}$. The zero-divisor graph of a finite commutative ring $R$ with unity, denoted by $Γ(R)$, is the simple graph whose vertices are all zero divisors of $R$ in which two vertices $u$ and $v$ are adjacent if and only if $uv = 0$ in $R$. In this paper, we investigate $L(2,1)$-labeling of some zero-divisor graphs. We study the partite truncation, a graph operation that allows us to obtain a reduced graph of relatively small order from a graph of significantly larger order. We establish the relation between $λ$-numbers of the graph and its partite truncated one. We make use of the operation partite truncation to contract the zero-divisor graph of a reduced ring to the zero-divisor graph of a Boolean ring.
