@article {
author = {Delfan, Abdolhossein and Rasouli, Hamid and Tehranian, Abolfazl},
title = {Intersection graphs associated with semigroup acts},
journal = {Categories and General Algebraic Structures with Applications},
volume = {11},
number = {Special Issue Dedicated to Prof. George A. Grätzer},
pages = {131-148},
year = {2019},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.11.1.131},
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.},
keywords = {$S$-act,intersection graph,Chromatic number,Clique number,weakly perfect graph},
url = {https://cgasa.sbu.ac.ir/article_76602.html},
eprint = {https://cgasa.sbu.ac.ir/article_76602_f65aa5a84b61acf36853ad0f3af7d2f7.pdf}
}