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The structure of zero-divisor semigroups with graph K n ○K 2
Authors:Tongsuo Wu  Fan Cheng
Institution:(1) Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, People’s Republic of China;(2) Department of Computer Science and Engineering, Shanghai Jiaotong University, Shanghai, 200240, People’s Republic of China
Abstract:This paper determines all commutative zero divisor semigroups whose zero divisor graph is a complete graph (finite or infinite), or a complete graph (finite or infinite) with one additional end vertex, and gives formulas for the numbers of all such semigroups with n elements. The research of T. Wu is supported by the National Natural Science Foundation of China (Grant No. 10671122) and the Natural Science Foundation of Shanghai (Grant No. 06ZR14049).
Keywords:Commutative zero-divisor semigroup  Complete graph  Complete graph with one end vertex  Counting formula
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