A New Near Octagon and the Suzuki Tower

We construct and study a new near octagon of order $(2,10)$ which has its full automorphism group isomorphic to the group $G_2(4):2$ and which contains $416$ copies of the Hall-Janko near octagon as full subgeometries. Using this near octagon and its substructures we give geometric constructions of the $G_2(4)$-graph and the Suzuki graph, both of which are strongly regular graphs contained in the Suzuki tower. As a subgeometry of this octagon we have discovered another new near octagon, whose order is $(2,4)$.

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On Some Combinatorial Structures Constructed from the Groups , , and

International Journal of Combinatorics ◽

10.1155/2011/137356 ◽

2011 ◽

Vol 2011 ◽

pp. 1-12

Author(s):

Dean Crnković ◽

Vedrana Mikulić Crnković

Keyword(s):

Automorphism Group ◽

Conjugacy Classes ◽

Maximal Subgroups ◽

Simple Groups ◽

Strongly Regular Graphs ◽

Regular Graphs ◽

Combinatorial Structures ◽

Full Automorphism Group ◽

Incidence Structures ◽

Strongly Regular

We describe a construction of primitive 2-designs and strongly regular graphs from the simple groups , and . The designs and the graphs are constructed by defining incidence structures on conjugacy classes of maximal subgroups of , and . In addition, from the group , we construct 2-designs with parameters and having the full automorphism group isomorphic to .

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The automorphism group of a class of strongly regular graphs related to Q(6,q)

European Journal of Combinatorics ◽

10.1016/j.ejc.2007.04.007 ◽

2008 ◽

Vol 29 (3) ◽

pp. 617-621

Author(s):

Stefaan De Winter ◽

Hendrik Van Maldeghem

Keyword(s):

Automorphism Group ◽

Strongly Regular Graphs ◽

Regular Graphs ◽

Strongly Regular

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Computer algebra investigation of known primitive triangle-free strongly regular graphs

10.29007/bdgp ◽

2018 ◽

Author(s):

Matan Ziv-Av ◽

Mikhail Klin

Keyword(s):

Automorphism Group ◽

Computer Algebra ◽

Computer Algebra Systems ◽

Strongly Regular Graphs ◽

Regular Graphs ◽

Computer Aided ◽

Strongly Regular ◽

Coherent Configurations

With the aid of computer algebra systems COCO and GAP withits packages we are investigating all seven known primitivetriangle-free strongly regular graphs on 5, 10, 16, 50, 56,77 and 100 vertices. These graphs are rank 3 graphs, havinga rich automorphism group. The embeddings of each graphfrom this family to other ones are described, theautomorphic equitable partitions are classified, allequitable partitions in the graphs on up to 50 vertices areenumerated. Basing on the reported computer aided resultsand using techniques of coherent configurations, a few newmodels of these graphs are suggested, which are relying onknowledge of just a small part of symmetries of a graph inconsideration.

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