ABSTRACT

For a simple connected graph G of order n, we obtain the distance signless Laplacian spectrum of the joined union of regular graphs $G_1,G_2,\dots ,G_n$ in terms of their adjacency spectrum and the spectrum of an auxiliary matrix. As a consequence, we obtain the distance signless Laplacian spectrum of the zero divisor graphs of finite commutative rings ${\mathbb{Z}}_n$ for some values of n. We show that $\mathrm{\Gamma }\left({\mathbb{Z}}_n\right)$ is not in general distance signless Laplacian integral for $n=p^z$, where p is any prime and $z\ge 2.$ Also, we find the spectrum of $\mathrm{\Gamma }\left({\mathbb{Z}}_{p^z}\right)$ for certain values of z.

中文翻译：

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关于ℤn的距离无符号拉普拉斯图谱和零因数图谱

摘要

对于一个简单的n阶连通图G，我们得到了正则图联合并集的距离无符号拉普拉斯谱$G_1,G_2,\dots ,G_n$根据它们的邻接谱和辅助矩阵的谱。因此，我们获得了有限交换环的零因数图的距离无符号拉普拉斯谱${\mathbb{Z}}_n$对于n的某些值。我们表明$\mathrm{\Gamma }\left({\mathbb{Z}}_n\right)$不是一般距离无符号拉普拉斯积分$n=p^z$, 其中p是任意素数并且$z\ge 2.$此外，我们发现频谱$\mathrm{\Gamma }\left({\mathbb{Z}}_{p^z}\right)$对于z的某些值。