Delfan, A., Rasouli, H., Tehranian, A. (2019). Intersection graphs associated with semigroup acts. Categories and General Algebraic Structures with Applications, 11(Special Issue Dedicated to Prof. George A. Grätzer), 131-148.

Abdolhossein Delfan; Hamid Rasouli; Abolfazl Tehranian. "Intersection graphs associated with semigroup acts". Categories and General Algebraic Structures with Applications, 11, Special Issue Dedicated to Prof. George A. Grätzer, 2019, 131-148.

Delfan, A., Rasouli, H., Tehranian, A. (2019). 'Intersection graphs associated with semigroup acts', Categories and General Algebraic Structures with Applications, 11(Special Issue Dedicated to Prof. George A. Grätzer), pp. 131-148.

Delfan, A., Rasouli, H., Tehranian, A. Intersection graphs associated with semigroup acts. Categories and General Algebraic Structures with Applications, 2019; 11(Special Issue Dedicated to Prof. George A. Grätzer): 131-148.

Intersection graphs associated with semigroup acts

^{1}Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran,

^{2}Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Abstract

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.

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