Subgroup-Chain Graphs

Abstract.

Starting from chains of subgroups in a group a construction for k-regular graphs is given and as an application of this construction a cubic graph of girth 20 with 6072 vertices is produced. This graph is exceptional in that, at the time of writing, it has fewest vertices for a cubic graph of this girth.

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Authors and Affiliations

1. School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

   Christopher Parker

2. Department of Mathematics, University of Manchester Institute of Science and Technology, P.O. Box 88, Manchester, M60 1QD, UK

   Peter Rowley

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1. Christopher Parker
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2. Peter Rowley
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Correspondence to Christopher Parker.

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Parker, C., Rowley, P. Subgroup-Chain Graphs. Graphs and Combinatorics 19, 537–545 (2003). https://doi.org/10.1007/s00373-003-0532-1

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• Received: 02 April 2002

• Issue Date: November 2003

• DOI: https://doi.org/10.1007/s00373-003-0532-1