On the inclusion graphs of \(S\)acts
Volume 18, Issue 3, pp 357363
http://dx.doi.org/10.22436/jmcs.018.03.10
Publication Date: July 22, 2018
Submission Date: November 23, 2017
Revision Date: January 10, 2018
Accteptance Date: January 30, 2018

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Authors
Abdolhossein Delfan
 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Hamid Rasouli
 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Abolfazl Tehranian
 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Abstract
In this paper, we define the inclusion graph \({\Bbb{Inc}}(A)\) of an \(S\)act \(A\) which is a graph whose vertices are nontrivial subacts of \(A\) and two distinct vertices \(B_1,B_2\) are adjacent if \(B_1 \subset B_2\) or \(B_2 \subset B_1\). We investigate the relationship between the algebraic properties of an \(S\)act \(A\) and the properties of the graph \(\Bbb{Inc}(A)\). Some properties of \(\Bbb{Inc}(A)\) including girth, diameter and connectivity are studied. We characterize some classes of graphs which are the inclusion graphs of \(S\)acts. Finally, some results concerning the domination number of such graphs are given.
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ISRP Style
Abdolhossein Delfan, Hamid Rasouli, Abolfazl Tehranian, On the inclusion graphs of \(S\)acts, Journal of Mathematics and Computer Science, 18 (2018), no. 3, 357363
AMA Style
Delfan Abdolhossein, Rasouli Hamid, Tehranian Abolfazl, On the inclusion graphs of \(S\)acts. J Math Comput SCIJM. (2018); 18(3):357363
Chicago/Turabian Style
Delfan, Abdolhossein, Rasouli, Hamid, Tehranian, Abolfazl. "On the inclusion graphs of \(S\)acts." Journal of Mathematics and Computer Science, 18, no. 3 (2018): 357363
Keywords
 \(S\)Act
 inclusion graph
 diameter
 girth
 domination number
MSC
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