A strongly regular decomposition of the complete graph and its association scheme

作者：Kharaghani Hadi; Sasani Sara; Suda Sho^*

来源：Finite Fields and Their Applications, 2017, 48: 356-370.

DOI：10.1016/j.ffa.2017.08.012

• Symmetric design
• Strongly regular graph
• Strongly regular decomposition
• Association scheme
• Generalized Hadamard matrix
• Symmetric Latin square

For any positive integer m, the complete graph on 2(2m)(2(m) +2) vertices is decomposed into 2(m)+1 commuting strongly regular graphs, which give rise to a symmetric association scheme of class 2(m+2) - 2. Furthermore, the eigenmatrices of the symmetric association schemes are determined explicitly. As an application, the eigenmatrix of the commutative strongly regular decomposition obtained from the strongly regular graphs is derived.

• 出版日期2017-11