scholarly journals 9. Cyclotomy, difference sets, sequences with low correlation, strongly regular graphs and related geometric substructures

2019 ◽  
pp. 173-198 ◽  
Author(s):  
Koji Momihara ◽  
Qi Wang ◽  
Qing Xiang
Keyword(s):  
Difference Sets ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Low Correlation ◽  
Strongly Regular

scholarly journals Switching of Edges in Strongly Regular Graphs I: A Family of Partial Difference Sets on 100 Vertices

10.37236/1710 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
L. K. Jørgensen ◽  
M. Klin
Keyword(s):  
Automorphism Groups ◽  
Difference Sets ◽  
Association Schemes ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Partial Difference ◽  
Galois Correspondence ◽  
Partial Difference Sets ◽  
Strongly Regular ◽  
Open Question

We present 15 new partial difference sets over 4 non-abelian groups of order 100 and 2 new strongly regular graphs with intransitive automorphism groups. The strongly regular graphs and corresponding partial difference sets have the following parameters: (100,22,0,6), (100,36,14,12), (100,45,20,20), (100,44,18,20). The existence of strongly regular graphs with the latter set of parameters was an open question. Our method is based on combination of Galois correspondence between permutation groups and association schemes, classical Seidel's switching of edges and essential use of computer algebra packages. As a by-product, a few new amorphic association schemes with 3 classes on 100 points are discovered.

scholarly journals New Regular Partial Difference Sets and Strongly Regular Graphs with Parameters (96,20,4,4) and (96,19,2,4)

10.37236/1114 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Anka Golemac ◽  
Joško Mandić ◽  
Tanja Vučičić
Keyword(s):  
Difference Sets ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Partial Difference ◽  
Symmetric Designs ◽  
Partial Difference Sets ◽  
Strongly Regular

New (96,20,4,4) and (96,19,2,4) regular partial difference sets are constructed, together with the corresponding strongly regular graphs. Our source are (96,20,4) regular symmetric designs.

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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