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\iteman{io-port 06092671}
\itemau{Dol\v{z}an, David; Oblak, Polona}
\itemti{The zero-divisor graphs of rings and semirings.}
\itemso{Int. J. Algebra Comput. 22, No. 4, 1250033, 20 p. (2012).}
\itemab
Summary: In this paper we study zero-divisor graphs of rings and semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We characterize all acyclic zero-divisor graphs of semirings and prove that in the case zero-divisor graphs are cyclic, their girths are less than or equal to 4. We find all possible cyclic zero-divisor graphs over commutative semirings having at most one 3-cycle, and characterize all complete $k$-partite and regular zero-divisor graphs. Moreover, we characterize all additively cancellative commutative semirings and all commutative rings such that their zero-divisor graph has exactly one 3-cycle.
\itemrv{~}
\itemcc{}
\itemut{ring; semiring; zero-divisor}
\itemli{doi:10.1142/S0218196712500336}
\end