Abstract
We describe two similar but independently-coded computations used to construct a complete catalogue of the transitive groups of degree less than 48, thereby verifying, unifying and extending the catalogues previously available. From this list, we construct all the vertex-transitive graphs of order less than 48. We then present a variety of summary data regarding the transitive groups and vertex-transitive graphs, focusing on properties that seem to occur most frequently in the study of groups acting on graphs. We illustrate how such catalogues can be used, first by finding a complete list of the elusive groups of order at most 47 and then by completely determining which groups of order at most 47 are CI groups.
Original language | English |
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Journal | Journal of Symbolic Computation |
DOIs | |
Publication status | E-pub ahead of print - 27 Jun 2019 |
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A census of small transitive groups and vertex-transitive graphs. / Holt, D.; Royle, Gordon.
In: Journal of Symbolic Computation, 27.06.2019.Research output: Contribution to journal › Article
TY - JOUR
T1 - A census of small transitive groups and vertex-transitive graphs
AU - Holt, D.
AU - Royle, Gordon
PY - 2019/6/27
Y1 - 2019/6/27
N2 - We describe two similar but independently-coded computations used to construct a complete catalogue of the transitive groups of degree less than 48, thereby verifying, unifying and extending the catalogues previously available. From this list, we construct all the vertex-transitive graphs of order less than 48. We then present a variety of summary data regarding the transitive groups and vertex-transitive graphs, focusing on properties that seem to occur most frequently in the study of groups acting on graphs. We illustrate how such catalogues can be used, first by finding a complete list of the elusive groups of order at most 47 and then by completely determining which groups of order at most 47 are CI groups.
AB - We describe two similar but independently-coded computations used to construct a complete catalogue of the transitive groups of degree less than 48, thereby verifying, unifying and extending the catalogues previously available. From this list, we construct all the vertex-transitive graphs of order less than 48. We then present a variety of summary data regarding the transitive groups and vertex-transitive graphs, focusing on properties that seem to occur most frequently in the study of groups acting on graphs. We illustrate how such catalogues can be used, first by finding a complete list of the elusive groups of order at most 47 and then by completely determining which groups of order at most 47 are CI groups.
KW - Cayley graph
KW - CI-group
KW - Computer enumeration
KW - Elusive group
KW - Transitive permutation group
KW - Vertex-transitive graph
UR - http://www.scopus.com/inward/record.url?scp=85068220356&partnerID=8YFLogxK
U2 - 10.1016/j.jsc.2019.06.006
DO - 10.1016/j.jsc.2019.06.006
M3 - Article
JO - Journal of Symbolic Computation
JF - Journal of Symbolic Computation
SN - 0747-7171
ER -