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Please use this identifier to cite or link to this item: https://www.um.edu.mt/library/oar/handle/123456789/111414
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dc.contributor.authorLauri, Josef-
dc.contributor.authorMizzi, Russell-
dc.contributor.authorScapellato, Raffaele-
dc.date.accessioned2023-07-10T06:11:41Z-
dc.date.available2023-07-10T06:11:41Z-
dc.date.issued2019-
dc.identifier.citationLauri, J., Mizzi, R., & Scapellato, R. (2019). The construction of a smallest unstable asymmetric graph and a family of unstable asymmetric graphs with an arbitrarily high index of instability. Discrete Applied Mathematics, 266, 85-91.en_GB
dc.identifier.issn18726771-
dc.identifier.urihttps://www.um.edu.mt/library/oar/handle/123456789/111414-
dc.description.abstractLet G be a graph. It is known that Aut(G) × Z2 is contained in Aut(G × K2) where G × K2 is the direct product of G with K2. When this inclusion is strict, the graph G is called unstable. We define the index of instability of G asen_GB
dc.description.abstract|Aut(G × K2)|en_GB
dc.description.abstract2|Aut(G)|en_GB
dc.description.abstractIn his paper (Wilson, 2008, p. 370),Wilson gave an example which at the time was known as a smallest asymmetric unstable graph. In this paper, we construct an even smaller unstable asymmetric graph (on twelve vertices), and show that it is a smallest unstable asymmetric (that is, with trivial automorphism group) graph. We then extend this method to build a family of unstable asymmetric graphs with an arbitrarily large index of instability.en_GB
dc.language.isoenen_GB
dc.publisherElsevier BVen_GB
dc.rightsinfo:eu-repo/semantics/restrictedAccessen_GB
dc.subjectAutomorphismsen_GB
dc.subjectIsomorphisms (Mathematics)en_GB
dc.subjectMathematics -- Graphic methodsen_GB
dc.titleThe construction of a smallest unstable asymmetric graph and a family of unstable asymmetric graphs with an arbitrarily high index of instabilityen_GB
dc.typearticleen_GB
dc.rights.holderThe copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder.en_GB
dc.description.reviewedpeer-revieweden_GB
dc.identifier.doi10.1016/j.dam.2018.10.026-
dc.publication.titleDiscrete Applied Mathematicsen_GB
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