S-系包含图
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摘要
设S是一个半群,M是S-系。M的包含图记为G(M),G(M)是无向简单图,它的顶点集由M的非平凡子系构成,顶点集中任意不同的两点是连接的当且仅当其中一个非平凡子系包含在另一个非平凡子系之中。基于该定义对这类图的完全性、连通性、直径、围长、团数和色数等性质进行了研究。
Let S be a semigroup and M be an S-act. The inclusion graph of M, denoted by G(M), is the undirected simple graph whose vertices are all non-trivial subact of M and defining two distinct vertices I and J to be adjacent if and only if I?J or J?I. Some results on completeness, connectivity, diameter, girth, the clique number and the chromatic number of G(M) are presented.
Let S be a semigroup and M be an S-act. The inclusion graph of M, denoted by G(M), is the undirected simple graph whose vertices are all non-trivial subact of M and defining two distinct vertices I and J to be adjacent if and only if I?J or J?I. Some results on completeness, connectivity, diameter, girth, the clique number and the chromatic number of G(M) are presented.
引文
[1] BECK I.Coloring of commutative rings[J].Algebra,1988,116(1):208-226.
[2] AKBARI S,HABIBI M,MAJIDINYAA A,et al.The inclusion ideal graph of rings[J].Communication in Algebra,2015,43(6):2457-2465.
[3] RASOULI H,TEHRANIAN A.Intersection graph of S-acts[J].Bulletin of the Malaysian Mathematical Sciences Society,2015,38(4):1575-1587.
[4] 刘仲奎.半群的S-系理论[M].2版.北京:科学出版社,1999.LIU Zhongkui.The S-act theory of semigroup[M].2nd ed.Beijing:Science Press,1999.
[5] 王朝瑞.图论[M].3版.北京:北京理工大学出版社,2004.WANG Chaorui.Graph theory[M].3rd ed.Beijing:Beijing Institute of Technology Press,2004.
[6] 张霞.S-系理论中若干问题的研究[D].广州:华南师范大学,2006.ZHANG Xia.Studies on some topics of S-act theory[D].Guangzhou:South China Normal University,2006.
[7] CHUDNOVSKY M,ROBERTSON N,SEYMOUR P,et al.The strong perfect graph theorem[J].Annals of Math,2006,164(1):51-229.
[2] AKBARI S,HABIBI M,MAJIDINYAA A,et al.The inclusion ideal graph of rings[J].Communication in Algebra,2015,43(6):2457-2465.
[3] RASOULI H,TEHRANIAN A.Intersection graph of S-acts[J].Bulletin of the Malaysian Mathematical Sciences Society,2015,38(4):1575-1587.
[4] 刘仲奎.半群的S-系理论[M].2版.北京:科学出版社,1999.LIU Zhongkui.The S-act theory of semigroup[M].2nd ed.Beijing:Science Press,1999.
[5] 王朝瑞.图论[M].3版.北京:北京理工大学出版社,2004.WANG Chaorui.Graph theory[M].3rd ed.Beijing:Beijing Institute of Technology Press,2004.
[6] 张霞.S-系理论中若干问题的研究[D].广州:华南师范大学,2006.ZHANG Xia.Studies on some topics of S-act theory[D].Guangzhou:South China Normal University,2006.
[7] CHUDNOVSKY M,ROBERTSON N,SEYMOUR P,et al.The strong perfect graph theorem[J].Annals of Math,2006,164(1):51-229.