TY - JOUR AU - Delfan, Abdolhossein AU - Rasouli, Hamid AU - Tehranian, Abolfazl PY - 2018 TI - On the inclusion graphs of \(S\)-acts JO - Journal of Mathematics and Computer Science SP - 357--363 VL - 18 IS - 3 AB - In this paper, we define the inclusion graph \({\Bbb{Inc}}(A)\) of an \(S\)-act \(A\) which is a graph whose vertices are non-trivial 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. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.018.03.10 DO - 10.22436/jmcs.018.03.10 ID - Delfan2018 ER - TY - JOUR TI - The inclusion ideal graph of rings AU - S. Akbari AU - M. Habibi AU - A. Majidinya AU - R. Manaviyat JO - Comm. Algebra PY - 2015 DA - 2015// VL - 43 ID - Akbari2015 ER - TY - JOUR TI - The total graph of a commutative ring AU - D. F. Anderson AU - A. Badawi JO - J. Algebra PY - 2008 DA - 2008// VL - 320 ID - Anderson2008 ER - TY - JOUR TI - The graphs of semigroups AU - J. Bosák JO - in: Theory of Graphs and its Application PY - 1964 DA - 1964// VL - 1964 ID - Bosák1964 ER - TY - JOUR TI - The graph of subgroups of a finite group AU - B. Csákány AU - G. Pollák JO - Czechoslovak Math. J. PY - 1969 DA - 1969// VL - 19 ID - Csákány1969 ER - TY - JOUR TI - Subspace inclusion graph of a vector space AU - A. Das JO - Comm. Algebra PY - 2016 DA - 2016// VL - 44 ID - Das2016 ER - TY - JOUR TI - Intersection graphs associated with semigroup acts AU - A. Delfan AU - H. Rasouli AU - A. Tehranian JO - PY - submitted DA - submitted// VL - ID - Delfansubmitted ER - TY - JOUR TI - The zero-divisor graph of a commutative semigroup AU - F. R. DeMeyer AU - T. McKenzie AU - K. Schneider JO - Semigroup Forum PY - 2002 DA - 2002// VL - 65 ID - DeMeyer2002 ER - TY - JOUR TI - Inclusion graph of subgroups of a group AU - P. Devi AU - R. Rajkumar JO - Cornell University Library PY - 2016 DA - 2016// VL - 2016 ID - Devi2016 ER - TY - JOUR TI - Zero divisor graphs for S-act AU - A. A. Estaji AU - T. Haghdadi AU - A. A. Estaji JO - Lobachevskii J. Math. PY - 2015 DA - 2015// VL - 36 ID - Estaji2015 ER - TY - BOOK TI - Monoids, Acts and Categories AU - M. Kilp AU - U. Knauer AU - A. V. Mikhalev PB - Walter de Gruyter & Co. PY - 2000 DA - 2000// CY - Berlin ID - Kilp2000 ER - TY - JOUR TI - Weakly perfect graphs arising from rings AU - H. R. Maimani AU - M. R. Pournaki AU - S. Yassemi JO - Glasg. Math. J. PY - 2010 DA - 2010// VL - 52 ID - Maimani2010 ER - TY - JOUR TI - The intersection graph of ideals of \(\mathbb{Z}_n\) is weakly perfect AU - R. Nikandish AU - M. J. Nikmehr JO - Cornell University Library PY - 2013 DA - 2013// VL - 2013 ID - Nikandish2013 ER - TY - JOUR TI - Intersection graphs of S-acts AU - H. Rasouli AU - A. Tehranian JO - Bull. Malays. Math. Sci. Soc. PY - 2015 DA - 2015// VL - 38 ID - Rasouli2015 ER - TY - JOUR TI - A sufficient condition for coinciding the Green graphs of semigroups AU - M. R. Sorouhesh AU - H. Doostie AU - C. M. Campbell JO - J. Math. Computer Sci. PY - 2017 DA - 2017// VL - 17 ID - Sorouhesh2017 ER - TY - BOOK TI - Introduction to Graph Theory AU - D. B. West PB - Prentice Hall PY - 2001 DA - 2001// CY - Upper Saddle River ID - West2001 ER -