### 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

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.

CLC Number:

• O152.7
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