Complement of Zero Divisors in Commutative Rings
碩士 === 國立中正大學 === 數學所 === 96 === Let $R$ be a commutative ring with identity and $Gamma(R)$ denotes its zero-divisor graph. We find all finite non-local rings $R$ such that $overline{Gamma(R)}$ have genus at most one, where $overline{Gamma(R)}$ denote the complement graph of $Gamma(R)$. We also find...
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| Format: | Others |
| Language: | en_US |
| Online Access: | http://ndltd.ncl.edu.tw/handle/61480295974135204392 |
| Summary: | 碩士 === 國立中正大學 === 數學所 === 96 === Let $R$ be a commutative ring with identity and $Gamma(R)$
denotes its zero-divisor graph. We find all finite non-local rings
$R$ such that $overline{Gamma(R)}$ have genus at most one, where
$overline{Gamma(R)}$ denote the complement graph of
$Gamma(R)$. We also find all finite rings $R$ of the forms
$mathbb{Z}_{p_1^{r_1}} imescdots imesmathbb{Z}_{p_k^{r_k}}$
such that $overline{Gamma(R)}$ have genus at most one.
Moreover, studies are done on the connectivity, girth and
Eulerian for $overline{Gamma(R)}$.
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