Zero-Divisor Semigroups of Fan-Shaped Graph
Received:March 25, 2010  Revised:October 03, 2010
Key Word: commutative zero-divisor semigroup   refinements of a star graph   fan-shaped graph   center.  
Fund ProjectL:Supported by the Guangxi Natural Science Foundation (Grant Nos.2010GXNSFB013048; 0991102; 2011GXNSFA018139) and the Scientific Research Foundation of Guangxi Educational Committee (Grant No.200911LX275).
Author NameAffiliation
Ke ZHOU School of Mathematical Sciences, Guangxi Teachers Education University, Guangxi 530023, P. R. China 
Hua Dong SU School of Mathematical Sciences, Guangxi Teachers Education University, Guangxi 530023, P. R. China 
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Abstract:
      Let $P_{n}$ be a path graph with $n$ vertices, and let $F_n=P_n\cup\{c\}$, where $c$ is adjacent to all vertices of $P_{n}$. The resulting graph is called a fan-shaped graph. The corresponding zero-divisor semigroups have been completely determined by Tang et al. for $n=2,3,4$ and by Wu et al. for $n\geq 6$, respectively. In this paper, we study the case for $n=5$, and give all the corresponding zero-divisor semigroups of $F_n$.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.05.019
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