Let $R$ be a nite non-commutative ring with center $Z(R)$. The commuting graph of $R$, denoted by $\Gamma_R$, is a simple undirected graph whose vertex set is $R\setminus Z(R)$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = yx$. Let$\Spec(\Gamma_R), \L-Spec(\GammaR)$ and $\Q-Spec(\GammaR)$ denote the spectrum, Laplacian spectrum and signless Laplacian spectrum of $\Gamma_R$ respectively. A nite non-commutative ring $R$ is called super integral if $\Spec(\Gamma_R), \L-Spec(Gamma_R)$ and $\Q-Spec(\Gamma_R)$ contain only integers. In this paper, we obtain several classes of super integral rings.
@article{39637,
title = {A note on super integral rings},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {38},
year = {2019},
doi = {10.5269/bspm.v38i4.39637},
language = {EN},
url = {http://dml.mathdoc.fr/item/39637}
}
Nath, Rajat Kanti. A note on super integral rings. Boletim da Sociedade Paranaense de Matemática, Tome 38 (2019) . doi : 10.5269/bspm.v38i4.39637. http://gdmltest.u-ga.fr/item/39637/