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Finite rings with some restrictions on zero-divisor graphs

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Abstract

The zero-divisor graph Γ(R) of an associative ring R is the graph whose vertices are all nonzero zero-divisors (one-sided and two-sided) of R, and two distinct vertices x and y are joined by an edge if and only if either xy = 0 or yx = 0.

In the present paper, we give full description of finite rings with regular zero-divisor graphs. We also prove some properties of finite rings such that their zero-divisor graphs satisfy the Dirac condition.

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Authors and Affiliations

  1. Altai State Pedagogical Academy, ul. Molodezhnaya 55, Barnaul, 656031, Russia

    A. S. Kuz’mina & Yu. N. Mal’tsev

Authors
  1. A. S. Kuz’mina
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  2. Yu. N. Mal’tsev
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Correspondence to A. S. Kuz’mina.

Additional information

Original Russian Text © A.S. Kuz’mina, Yu.N. Mal’tsev, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 12, pp. 48–59.

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Kuz’mina, A.S., Mal’tsev, Y.N. Finite rings with some restrictions on zero-divisor graphs. Russ Math. 58, 41–50 (2014). https://doi.org/10.3103/S1066369X14120056

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  • DOI: https://doi.org/10.3103/S1066369X14120056

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