The structure of zero-divisor semigroups with graph K
n
○K
2 |
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Authors: | Tongsuo Wu Fan Cheng |
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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 |
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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). |
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Keywords: | Commutative zero-divisor semigroup Complete graph Complete graph with one end vertex Counting formula |
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