TY - JOUR ID - 76602 TI - Intersection graphs associated with semigroup acts JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Delfan, Abdolhossein AU - Rasouli, Hamid AU - Tehranian, Abolfazl AD - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, AD - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran AD - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Y1 - 2019 PY - 2019 VL - 11 IS - Special Issue Dedicated to Prof. George A. Grätzer SP - 131 EP - 148 KW - $S$-act KW - intersection graph KW - Chromatic number KW - Clique number KW - weakly perfect graph DO - 10.29252/cgasa.11.1.131 N2 - < 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. UR - https://cgasa.sbu.ac.ir/article_76602.html L1 - https://cgasa.sbu.ac.ir/article_76602_f65aa5a84b61acf36853ad0f3af7d2f7.pdf ER -