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Intersection Graphs of \(S\)-Acts

Abstract

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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Acknowledgments

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.

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Correspondence to H. Rasouli.

Additional information

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

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Keywords

  • \(S\)-act
  • Intersection graph
  • Connectivity
  • Diameter
  • Girth

Mathematics Subject Classification

  • 20M30
  • 05C25
  • 05C40
  • 58E40