Intersection graphs of \(S\)-acts
type: Item
instance of: scholarly article
title: Intersection graphs of \(S\)-acts
zbMATH Open document ID: 1351.20036
author: Hamid Rasouli
author: Abolfazl Tehranian
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2015-10-15T00:00:00Z
review text: The intersection graph \(G(A)\) of an \(S\)-act \(A\) is undirected, has the non-trivial subacts of \(A\) as vertices, two of which are adjacent if their intersection is non-empty. Let \(S\) be a monoid. The authors prove for example: If \(G(A)\) is connected then \(\mathrm{diam}(G(A))\leq 2\), if it contains a cycle then \(\mathrm{girth}(G(A))=3\). Suppose that \(A\) is non-cyclic. If \(A\) is free or projective then \(G(A)\) is connected iff \(|G(A)|\geq 6\), in this case \(\mathrm{diam}(G(A))= 2\) and \(\mathrm{girth}(G(A))=3\). Similar results are presented if \(S\) is a group.
reviewed by: Ulrich Knauer
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 6494660
zbMATH Keywords: \(S\)-act
zbMATH Keywords: intersection graph
zbMATH Keywords: connectivity
zbMATH Keywords: diameter
zbMATH Keywords: girth
MaRDI profile type: Publication
full work available at URL: s40840-014-0098-5
OpenAlex ID: W1981185530
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DOI: 10.1007/S40840-014-0098-5
description: scientific article; zbMATH DE number 6494660