JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (8): 121-126.doi: 10.6040/j.issn.1671-9352.0.2018.504

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The inclusion graph of S-acts

SUN Shuang, LIU Hong-xing*   

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, Shandong, China
  • Online:2019-08-20 Published:2019-07-03

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Abstract: 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.

Key words: S-act, inclusion graph, diameter, girth, clique number, chromatic number

CLC Number: 

  • O152.7
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