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Search: MSC category 13M99
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1. CMB Online first
 Dolžan, David

The metric dimension of the total graph of a finite commutative ring
We study the total graph of a finite commutative ring. We calculate
its metric dimension in the case when the Jacobson radical of
the ring is nontrivial and we examine the metric dimension of
the total graph of a product of at most two fields, obtaining
either exact values in some cases or bounds in other, depending
on the number of elements in the respective fields.
Keywords:total graph, finite ring, metric dimension Categories:13M99, 05E40 

2. CMB 2011 (vol 55 pp. 127)
 LaGrange, John D.

Characterizations of Three Classes of ZeroDivisor Graphs
The zerodivisor graph $\Gamma(R)$ of a commutative ring $R$ is the graph whose vertices consist of
the nonzero zerodivisors 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 zerodivisor graphs of Boolean
rings. Also, commutative rings $R$ such that
$\Gamma(R)$ is isomorphic to the zerodivisor graph of a direct product of integral domains are classified, as well as
those whose zerodivisor graphs are central vertex complete.
Categories:13A99, 13M99 
