Faster isomorphism testing of strongly regular graphs
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Cycle Switches in Latin Squares
Graphs and Combinatorics
Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)
Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
The Cycle Switching Graph of the Steiner Triple Systems of Order 19 is Connected
Graphs and Combinatorics
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The block graph of a Steiner triple system of order v is a (v(v-1)/6,3(v-3)/2,(v+3)/2,9) strongly regular graph. For large v, every strongly regular graph with these parameters is the block graph of a Steiner triple system, but exceptions exist for small orders. An explanation for some of the exceptional graphs is here provided via the concept of switching. (Group divisible designs corresponding to) Latin squares are also treated in an analogous way. Many new strongly regular graphs are obtained by switching and by constructing graphs with prescribed automorphisms. In particular, new strongly regular graphs with the following parameters that do not come from Steiner triple systems or Latin squares are found: (49,18,7,6), (57,24,11,9), (64,21,8,6), (70,27,12,9), (81,24,9,6), and (100,27,10,6).