Book thickness of toroidal zero-divisor graphs
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DOI: 10.1007/s13370-017-0487-7
Abstract: We determine the book thickness of all zero-divisor graphs with genus at most one. We also describe four families of three page embeddable zero-divisor graphs. read more here.
Keywords: book thickness; zero divisor; divisor graphs;
Beck’s Zero-Divisor Graph in the Realm of Signed Graph
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DOI: 10.1007/s40009-019-00836-8
Abstract: For a commutative ring R with unity ( $$1\ne 0$$ 1 ≠ 0 ), the zero-divisor graph of R , denoted by $$\varGamma (R)$$ Γ ( R ) , is a simple graph with vertices… read more here.
Keywords: divisor graph; zero divisor; beck zero; graph realm ... See more keywords
Classification of nonlocal rings with genus one 3-zero-divisor hypergraphs
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DOI: 10.1080/00927872.2016.1206344
Abstract: ABSTRACT Let R be a commutative ring with identity and let Z(R,k) be the set of all k-zero-divisors in R and k>2 an integer. The k-zero-divisor hypergraph of R, denoted by ℋk(R), is a hypergraph… read more here.
Keywords: genus one; classification nonlocal; zero divisor; rings genus ... See more keywords
On zero-divisor graphs of skew polynomial rings over non-commutative rings
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DOI: 10.1142/s0219498817500566
Abstract: In this paper, we continue to study zero-divisor properties of skew polynomial rings R[x; α,δ], where R is an associative ring equipped with an endomorphism α and an α-derivation δ. For an associative ring R,… read more here.
Keywords: divisor graphs; graphs skew; zero divisor; polynomial rings ... See more keywords
The zero-divisor graph of a ring with involution
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DOI: 10.1142/s0219498818500500
Abstract: For a *-ring A, we associate a simple undirected graph Γ*(A) having all nonzero left zero-divisors of A as vertices and, two vertices x and y are adjacent if xy* = 0. In case of… read more here.
Keywords: divisor graph; zero divisor; graph ring; ring involution ... See more keywords
Classification of posets using zero-divisor graphs
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DOI: 10.1515/ms-2017-0076
Abstract: Abstract Halaš and Jukl associated the zero-divisor graph G to a poset (X,≤) with zero by declaring two distinct elements x and y of X to be adjacent if and only if there is no… read more here.
Keywords: divisor graphs; classification posets; zero divisor; divisor ... See more keywords
Zero-divisor graphs of partial transformation semigroups
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DOI: 10.3906/mat-2012-94
Abstract: Let Pn be the partial transformation semigroup on Xn = {1, 2, . . . , n} . In this paper, we find the left zerodivisors, right zero-divisors and two sided zero-divisors of Pn ,… read more here.
Keywords: graphs partial; divisor graphs; zero divisor; transformation ... See more keywords
On the offensive alliance number for the zero divisor graph of $ \mathbb{Z}_n $
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DOI: 10.3934/mbe.2023539
Abstract: A nonempty subset $ D $ of vertices in a graph $ \Gamma = (V, E) $ is said is an offensive alliance, if every vertex $ v \in \partial(D) $ satisfies $ \delta_D(v) \geq… read more here.
Keywords: offensive alliance; alliance number; gamma; zero divisor ... See more keywords