论文标题
$ \ mathbb {z} _ {n} $的comaximal图的拉普拉斯谱
Laplacian Spectra of Comaximal Graph of $\mathbb{Z}_{n}$
论文作者
论文摘要
本文着重于查找comaximal Graph $γ（\ Mathbb Z_n）$ $ \ Mathbb Z_n $的comaximal Graph $γ（\ Mathbb Z_N）$的特征值$ n> 2 $。我们为各种$ n $确定$γ（\ mathbb z_n）$的特征值，还提供了一个程序，以查找$γ（\ Mathbb z_n）$的特征值。我们表明$γ（\ Mathbb z_n）$是$ n = p^αq^β$的laplacian积分，其中$ p，q $是primes，$α，$α，β$是非阴性整数。 $γ（\ Mathbb z_n）$的代数和顶点连接已显示为所有$ n> 2 $。已经获得了第二大特征值$γ（\ Mathbb z_n）$的上限，并且还确定了其平等的必要条件。最后，我们讨论了频谱半径的多样性以及$γ（\ Mathbb Z_N）$的代数连接性的多样性。在本文末尾讨论了一些问题，以进行进一步研究。
This article focuses on finding the eigenvalues of the Laplacian matrix of the comaximal graph $Γ(\mathbb Z_n)$ of the ring $\mathbb Z_n$ for $n> 2$. We determine the eigenvalues of $Γ(\mathbb Z_n)$ for various $n$ and also provide a procedure to find the eigenvalues of $Γ(\mathbb Z_n)$ for any $n> 2$. We show that $Γ(\mathbb Z_n)$ is Laplacian Integral for $n=p^αq^β$ where $p,q$ are primes and $α, β$ are non-negative integers. The algebraic and vertex connectivity of $Γ(\mathbb Z_n)$ have been shown to be equal for all $n> 2$. An upper bound on the second largest eigenvalue of $Γ(\mathbb Z_n)$ has been obtained and a necessary and sufficient condition for its equality has also been determined. Finally we discuss the multiplicity of the spectral radius and the multiplicity of the algebraic connectivity of $Γ(\mathbb Z_n)$. Some problems have been discussed at the end of this article for further research.
