The Zero-Divisor Graphs of Rings and Semirings

  title={The Zero-Divisor Graphs of Rings and Semirings},
  author={David Dolzan and Polona Oblak},
In this paper we study zero-divisor graphs of rings and semirings. We show that all zerodivisor 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… CONTINUE READING

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