论文标题
在cozero划线图上，凸起了环
On the cozero-divisor graphs assosciated to rings
论文作者
论文摘要
让$ r $成为团结的戒指。 $γ'（r）$表示的环$ r $的cozero-divisor图是一个无向的简单图形，其顶点是$ r $的所有非零和非单元元素的集合，而两个不同的顶点$ x $和$ $仅在$ x $ x $ x $ x \ notin ry $ y $ y y y y ynos y ynodin ry $ y \ ynin rx n n.nof y n n ry \ y n n n ry \ ynos ry \ notin r x n.notin ry \ ynon rx n ry \ ynon rx n ry \ yninn rx。在本文中，首先我们研究$γ'（\ Mathbb {z} _n）$的拉普拉斯频谱。我们表明图形$γ'（\ Mathbb {z} _ {pq}）$是laplacian积分。此外，我们获得了$γ'（\ Mathbb {z} _n）$的laplacian频谱，以$ n = p^{n_1} q^{n_2} $，其中$ n_1，n_1，n_2 \ in \ mathbb {n} $ {n} $和$ p，$ p，q $是不同的普rime。为了研究$γ'（\ Mathbb {z} _n）$的拉普拉斯光谱半径和代数连接性，我们表征了$ n $的值，$ n $的laplacian光谱半径等于$γ'（\ mathbb {z} _n）$。此外，还描述了$γ'（\ Mathbb {z} _n）$ comincide的代数连接和顶点连接的$ n $的值。在本文的最后一部分中，我们获得了$γ'（\ Mathbb {z} _n）$的Wiener索引，以进行任意$ n $。
Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$, denoted by $Γ'(R)$, is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $x \notin Ry$ and $y \notin Rx$. In this paper, first we study the Laplacian spectrum of $Γ'(\mathbb{Z}_n)$. We show that the graph $Γ'(\mathbb{Z}_{pq})$ is Laplacian integral. Further, we obtain the Laplacian spectrum of $Γ'(\mathbb{Z}_n)$ for $n = p^{n_1}q^{n_2}$, where $n_1, n_2 \in \mathbb{N}$ and $p, q$ are distinct primes. In order to study the Laplacian spectral radius and algebraic connectivity of $Γ'(\mathbb{Z}_n)$, we characterized the values of $n$ for which the Laplacian spectral radius is equal to the order of $Γ'(\mathbb{Z}_n)$. Moreover, the values of $n$ for which the algebraic connectivity and vertex connectivity of $Γ'(\mathbb{Z}_n)$ coincide are also described. At the final part of this paper, we obtain the Wiener index of $Γ'(\mathbb{Z}_n)$ for arbitrary $n$.
