Let \(S\) be a semigroup. The intersection graph of an \(S\)-act \(A\), denoted by \(G(A)\), is the undirected simple graph obtained by setting all non-trivial subacts of \(A\) to be the vertices and defining two distinct vertices to be adjacent if and only if their intersection is non-empty. It investigated the interplay between the algebraic properties of \(A\) and the graph-theoretic properties of \(G(A)\). Also some characterization results regarding connectivity, completeness, diameter, and girth of \(G(A)\) are presented.
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The authors gratefully appreciate the referee’s careful reading of the paper and useful comments. Also, we acknowledge the financial support of Islamic Azad University.
Communicated by Xueliang Li.
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Rasouli, H., Tehranian, A. Intersection Graphs of \(S\)-Acts. Bull. Malays. Math. Sci. Soc. 38, 1575–1587 (2015). https://doi.org/10.1007/s40840-014-0098-5
- Intersection graph
Mathematics Subject Classification