| 图的字典序积和自同态幺半群 |
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| 引用本文： | 樊锁海.图的字典序积和自同态幺半群[J].数学学报,1995,38(2):248-252. |
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| 作者姓名： | 樊锁海 |
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| 作者单位： | 暨南大学数学系 |
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| 摘 要： | Ｆ．Ｈａｒａｒｙ￣［１］和Ｇ．Ｓａｂｉｄｕｓｓｉ￣［２］考虑过图Ｘ和ｙ的字典序积Ｘ［Ｙ］的自同构群ＡｕｔＸ［Ｙ］与它们各自的自同构群的圈积ＡｕｔＸ［ＡｕｔＹ］的关系，并给出了两者相等的一种刻划．在本文，我们考虑更广意义上的问题，即Ｘ［Ｙ］的自同态幺半群ＥｎｄＸ［Ｙ］与各自的自同态幺半群的圈积ＥｎｄＸ［ＥｎｄＹ］的关系，也给出了两者相等的一种刻划，同时得到了下面结果：如果Ｘ和Ｙ都是不含Ｋ＿３导出子图的连通图，且其中之一图有奇数围长，那么ＥｎｄＸ［Ｙ］＝ＥｎｄＸ［ＥｎｄＹ］．
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| 关 键 词： | 图，字典序积，自同态，幺半群，圈积 |
| 收稿时间： | 1992-12-25 |
| 修稿时间： | 1993-12-1 |
The Endomorphism Monoids of the Lexicographic Product of Two Graphs |
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| Fan Suohai.The Endomorphism Monoids of the Lexicographic Product of Two Graphs[J].Acta Mathematica Sinica,1995,38(2):248-252. |
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| Authors: | Fan Suohai |
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| Institution: | Fan Suohai (Department of Mathematics, Ji'nan Unisversity,Guangzhou 510631 China) |
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| Abstract: | The criterions for the automorphism group of the lexicographic products of two and G. Sabidussi￣2].In this paper, the corresponding criterion for endomorphism monlid is given. In the meantime, the following result is obtained:If X and Y are K￣3 free connectedgraphs, and either of two graphs has odd girth,then the endomorphism monoid End XY] of the lexicographic product XY]of X and Y coincides with the wreath product End X End Y]Of their monoid End Xand End Y. |
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| Keywords: | graph lexicogaphic product endomorphism monoid wreath product |
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