Intersection graphs associated with semigroup acts
Publish Year: 1398
Type: Journal paper
Language: English
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Document National Code:
JR_CGASAT-11-0_006
Index date: 14 September 2021
Intersection graphs associated with semigroup acts abstract
< p>The intersection graph \\mathbb{Int}(A) of an S-act A over a semigroup S is an undirected simple graph whose vertices are non-trivial subacts of A, and two distinct vertices are adjacent if and only if they have a non-empty intersection. In this paper, we study some graph-theoretic properties of \\mathbb{Int}(A) in connection to some algebraic properties of A. It is proved that the finiteness of each of the clique number, the chromatic number, and the degree of some or all vertices in \\mathbb{Int}(A) is equivalent to the finiteness of the number of subacts of A. Finally, we determine the clique number of the graphs of certain classes of S-acts.
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Intersection graphs associated with semigroup acts authors
Abdolhossein Delfan
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran,
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
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