The n-zero-divisor graph of a commutative semigroup
Let S be a (multiplicative) commutative semigroup with 0, Z(S) the set of zero-divisors of S, and n a positive integer. The zero-divisor graph of S is the (simple) graph Γ(S) with vertices Z(S) ∗ = Z(S) \ {0}, and distinct vertices x and y are adjacent if and only if xy = 0. In this paper, we introd...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2022
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/25070 |
| الوسوم: |
إضافة وسم
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| الملخص: | Let S be a (multiplicative) commutative semigroup with 0, Z(S) the set of zero-divisors of S, and n a positive integer. The zero-divisor graph of S is the (simple) graph Γ(S) with vertices Z(S) ∗ = Z(S) \ {0}, and distinct vertices x and y are adjacent if and only if xy = 0. In this paper, we introduce and study the n-zero-divisor graph of S as the (simple) graph Γn(S) with vertices Zn(S) ∗ = {x n | x ∈ Z(S)} \ {0}, and distinct vertices x and y are adjacent if and only if xy = 0. Thus each Γn(S) is an induced subgraph of Γ(S) = Γ1(S). We pay particular attention to diam(Γn(S)), gr(Γn(S)), and the case when S is a commutative ring with 1 6= 0. We also consider several other types of “n-zero-divisor” graphs and commutative rings such that some power of every element (or zero-divisor) is idempotent. |
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