scholarly journals On Some Combinatorial Structures Constructed from the Groups , , and

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 .

scholarly journals A New Near Octagon and the Suzuki Tower

10.37236/5067 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Anurag Bishnoi ◽  
Bart De Bruyn
Keyword(s):  
Automorphism Group ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Geometric Constructions ◽  
Full Automorphism Group ◽  
Strongly Regular

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 $(2,4)$.

scholarly journals Cyclotomic Trace Codes

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 168
Author(s):  
Dean Crnković ◽  
Andrea Švob ◽  
Vladimir D. Tonchev
Keyword(s):  
Quantum Codes ◽  
Strongly Regular Graphs ◽  
Block Designs ◽  
Regular Graphs ◽  
Combinatorial Structures ◽  
Trace Codes ◽  
Strongly Regular ◽  
Projective Codes

A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers ( s ≥ 2 ) of all nonzero elements in G F ( p m ) , where p ≥ 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over G F ( 4 ) that give rise to optimal or near optimal quantum codes. In addition, the codes yield interesting combinatorial structures, such as strongly regular graphs and block designs.

scholarly journals 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.

On extensions of small strongly regular graphs with eigenvalue 3

2015 ◽  
Vol 92 (1) ◽  
pp. 482-486
Author(s):  
A. A. Makhnev ◽  
D. V. Paduchikh
Keyword(s):  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular

On triple systems and strongly regular graphs

2012 ◽  
Vol 119 (7) ◽  
pp. 1414-1426 ◽  
Author(s):  
Majid Behbahani ◽  
Clement Lam ◽  
Patric R.J. Östergård
Keyword(s):  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Triple Systems ◽  
Strongly Regular
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