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Tongsuo Wu

Publications and source records attributed to Tongsuo Wu.

23 records · Page 2Linked to original sources
arXiv2005

Simple Graphs and Commutative Zero-Divisor Semigroups

In this paper, we study commutative zero-divisor semigroups determined by graphs. We prove a uniqueness theorem for a class of graphs. We show two classes of graphs that have no corresponding semigroups. In particular, any complete graph $K_n$ together with more than three end vertices and any complete bipartite graph together with more than one end vertices have no corresponding semigroups. We also determine all possible zero-divisor semigroups whose zero-divisor graph is the com- plete graph $K_3$ together with two end vertices.

math.RA↗
arXiv2005

Sub-semigroups determined by the zero-divisor graph

In this paper we study sub-semigroups of a zero-divisor semigroup $S$ determined by properties of the zero-divisor graph $Γ(S)$. We use these sub-semigroups to study the correspondence between zero- divisor semigroups and zero-divisor graphs. We study properties of sub- semigroups of Boolean semigroups via the zero-divisor graph. As an application, we provide a characterization of the graphs which are zero- divisor graphs of Boolean rings.

math.RA↗
arXiv2005

The Structures of Zero-divisor Semigroups with Graph Kn + 1

In this paper, we determine the structures of zero-divisor semigroups whose graph is $K_n + 1$, the complete graph $K_n$ together with an end vertex. We also present a formula to calculate the number of non-isomorphic zero-divisor semigroups corresponding to the complete graph $K_n$, for all positive integer $n$.

math.RA↗
arXiv2004

On directed zero-divisor graphs of finite rings

For an artinian ring $R$, the directed zero-divisor graph $Γ(R)$ is connected if and only if there is no proper one-sided identity element in $R$. Sinks and sources are characterized and clarified for finite ring $R$, especially, it is proved that for {\it any} ring $R$, if there exists a source $b$ in $Γ(R)$ with $b^2=0$, then $|R|=4$ and $R=\{0,a,b,c\}$, where $a$ and $c$ are left identity elements and $ba=0=bc$. Such a ring $R$ is also the only ring such that $Γ(R) $ has exactly one source. This shows that $Γ(R)$ can not be a network for any ring $R$.

math.RA↗