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Characterizations of Three Classes of Zero-Divisor Graphs |
Canad. Math. Bull. 55(2012), 127-137
Published:2011-05-30
Printed: Mar 2012
Printed: Mar 2012
- John D. LaGrange,
Abstract
The zero-divisor graph $\Gamma(R)$ of a commutative ring $R$ is the graph whose vertices consist of
the nonzero zero-divisors of $R$ such that distinct vertices $x$ and
$y$ are adjacent if and only if $xy=0$. In this paper,
a characterization is provided for zero-divisor graphs of Boolean
rings. Also, commutative rings $R$ such that
$\Gamma(R)$ is isomorphic to the zero-divisor graph of a direct product of integral domains are classified, as well as
those whose zero-divisor graphs are central vertex complete.
| MSC Classifications: |
13A99 - None of the above, but in this section 13M99 - None of the above, but in this section |