%0 Journal Article
%T Intersection graphs associated with semigroup acts
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Delfan, Abdolhossein
%A Rasouli, Hamid
%A Tehranian, Abolfazl
%D 2019
%\ 07/01/2019
%V 11
%N Special Issue Dedicated to Prof. George A. Grätzer
%P 131-148
%! Intersection graphs associated with semigroup acts
%K $S$-act
%K intersection graph
%K Chromatic number
%K Clique number
%K weakly perfect graph
%R 10.29252/cgasa.11.1.131
%X < 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.
%U https://cgasa.sbu.ac.ir/article_76602_f65aa5a84b61acf36853ad0f3af7d2f7.pdf