Intersection graphs associated with semigroup acts | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 9، دوره 11، Special Issue Dedicated to Prof. George A. Grätzer، مهر 2019، صفحه 131-148 اصل مقاله (647.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.11.1.131 | ||
| نویسندگان | ||
| Abdolhossein Delfan1؛ Hamid Rasouli* 2؛ Abolfazl Tehranian2 | ||
| 1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, | ||
| 2Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | ||
| چکیده | ||
| < 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. | ||
| کلیدواژهها | ||
| $S$-act؛ intersection graph؛ chromatic number؛ clique number؛ weakly perfect graph | ||
| مراجع | ||
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