Co-intersection graph of subacts of an act

Document Type : Research Paper

Authors

1 Department of Mathematics, Khorramabad Branch, Islamic Azad University, Iran

2 Department of Mathematics, Science and Research Branch , Islamic Azad University, Tehran, Iran

3 Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran

Abstract

In this paper, we define the co-intersection graph $G(A)$ of an \(S\)-act \(A\) which is a graph whose vertices are non-trivial subacts of \(A\) and two  distinct  vertices \(B_1\) and \( B_2\) are adjacent if \(B_1 \cup B_2\neq A\).  We investigate the relationship between the algebraic properties of an  \(S\)-act \(A\) and the properties of the graph $G(A)$.
 

Keywords

References

1. A. Delfan, H. Rasouli and A. Tehranian, A new class of weakly perfect graphs attached to S-acts, JP J. Algebra, Number Theory Appl. (5) 40 (2018), 775-785.
2. A. Delfan, H. Rasouli and A. Tehranian, On the inclusion graphs of S-acts, J. Math. Computer Sci. (4) 18 (2018), 357-363.
3. A. Delfan, H. Rasouli and A. Tehranian, Intersection graphs associated with semigroup acts, Categ. Gen. Algebr. Struct. Appl. 11 (2019), 131-148.
4. A.A. Estaji and A. Haghdadi, Zero divisor graphs for S-act, Lobachevskii J. Math. (1) 36 (2015), 1-8.
5. M. Kilp, U. Knauer and A.V. Mikhalev, Monoids, Acts and Categories. de Gruyter Expositions in Mathematics, 29. de Gruyter, Berlin, 2000.
6. L. A. Mahdavi and Y. Talebi, Co-intersection graph of submodules of module, Algebra Discrete Math, (1) 21 (2016), 128-143.
7. L. A. Mahdavi and Y. Talebi, Properties of Co-intersection graph of submodules of a module, J. Prime Res. Math. 13 (2017), 16-29.
8. H. Rasouli and A. Tehranian, Intersection graphs of S-acts, Bull. Malays. Math. Sci. Soc. (4) 38 (2015), 1575-1587.
9. D. B. West, Introduction to Graph Theory. Prentice Hall, 2001.
Journal of Algebra and Related Topics
Volume 10, Issue 2
December 2022
Pages 1-12

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