Intersection graphs associated with semigroup acts

نویسندگان

  • Abdolhossein Delfan Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran,
  • Abolfazl Tehranian 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
چکیده مقاله:

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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عنوان ژورنال

دوره 11  شماره Special Issue Dedicated to Prof. George A. Grätzer

صفحات  131- 148

تاریخ انتشار 2019-07-01

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