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 -