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Links between two semisymmetric graphs on 112 vertices via association schemes

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Title: Links between two semisymmetric graphs on 112 vertices via association schemes
Authors: Klin, Mikhail, Lauri, Josef, Ziv-Av, Matan
Publisher Information: Elsevier
Publication Year: 2012
Collection: University of Malta: OAR@UM / L-Università ta' Malta
Subject Terms: Mathematics -- Graphic methods, Algebra -- Data processing, Graph theory -- Mathematical models, Association schemes (Combinatorial analysis)
Description: This paper provides a model of the use of computer algebra experimentation in algebraic graph theory. Starting from the semisymmetric cubic graph L on 112 vertices, we embed it into another semisymmetric graph N of valency 15 on the same vertex set. In order to consider systematically the links between L and N, a number of combinatorial structures are involved and related coherent configurations are investigated. In particular, the construction of the incidence double cover of directed graphs is exploited. As a natural by-product of the approach presented here, a number of new interesting (mostly non-Schurian) association schemes on 56, 112 and 120 vertices are introduced and briefly discussed. We use computer algebra system GAP (including GRAPE and nauty), as well as computer package COCO. ; peer-reviewed
Document Type: article in journal/newspaper
Language: English
Relation: https://www.um.edu.mt/library/oar/handle/123456789/45992
DOI: 10.1016/j.jsc.2011.12.040
Availability: https://www.um.edu.mt/library/oar/handle/123456789/45992
https://doi.org/10.1016/j.jsc.2011.12.040
Rights: info:eu-repo/semantics/restrictedAccess ; The 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.
Accession Number: edsbas.60B07C5D
Database: BASE
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  Data: Links between two semisymmetric graphs on 112 vertices via association schemes
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  Data: <searchLink fieldCode="AR" term="%22Klin%2C+Mikhail%22">Klin, Mikhail</searchLink><br /><searchLink fieldCode="AR" term="%22Lauri%2C+Josef%22">Lauri, Josef</searchLink><br /><searchLink fieldCode="AR" term="%22Ziv-Av%2C+Matan%22">Ziv-Av, Matan</searchLink>
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  Data: 2012
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  Data: <searchLink fieldCode="DE" term="%22Mathematics+--+Graphic+methods%22">Mathematics -- Graphic methods</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra+--+Data+processing%22">Algebra -- Data processing</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory+--+Mathematical+models%22">Graph theory -- Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Association+schemes+%28Combinatorial+analysis%29%22">Association schemes (Combinatorial analysis)</searchLink>
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  Data: This paper provides a model of the use of computer algebra experimentation in algebraic graph theory. Starting from the semisymmetric cubic graph L on 112 vertices, we embed it into another semisymmetric graph N of valency 15 on the same vertex set. In order to consider systematically the links between L and N, a number of combinatorial structures are involved and related coherent configurations are investigated. In particular, the construction of the incidence double cover of directed graphs is exploited. As a natural by-product of the approach presented here, a number of new interesting (mostly non-Schurian) association schemes on 56, 112 and 120 vertices are introduced and briefly discussed. We use computer algebra system GAP (including GRAPE and nauty), as well as computer package COCO. ; peer-reviewed
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  Data: info:eu-repo/semantics/restrictedAccess ; The 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.
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