Type-II Matrices Attached to Conference Graphs
Ada Chan
and Rie Hosoya
DOI: 10.1023/B:JACO.0000048520.23243.ce
Abstract
We determine the Nomura algebras of the type-II matrices belonging to the Bose-Mesner algebra of a conference graph.
Pages: 341–351
Keywords: association schemes; Bose-mesner algebras; nomura algebras; spin models; type II matrices
Full Text: PDF
References
1. E. Bannai and E. Bannai, “Generalized generalized spin models (four-weight spin models),” Pacific J. Math. 170(1) (1995), 1-16.
2. E. Bannai and T. Ito, Algebraic Combinatorics. I. Association Schemes, Benjamin/Cummings Publisher Co., Inc., Menlo Park, Calif., 1984.
3. A.E. Brouwer, “Strongly regular graphs,” in The CRC Handbook of Combinatorial Designs, C.J. Colbourn and J.H. Dinitz (Eds.), CRC Press, Boca Raton, 1996, pp. 667-683.
4. C.D. Godsil, Algebraic Combinatorics, Chapman & Hall, New York, 1993.
5. C.D. Godsil, “Type II matrices and Jones pairs,”
2001. Preprints.
6. C.D. Godsil and A. Chan, “Strongly regular graphs and type II matrices,”
2001. Preprints.
7. R. Hosoya and H. Suzuki, “Type II matrices and their Bose-Mesner algebras,” J. Algebraic Combin. 17 (2003), 19-37.
8. F. Jaeger, “Strongly regular graphs and spin models for the Kauffman polynomial,” Geom. Dedicata 44 (1992), 23-52.
9. F. Jaeger, M. Matsumoto, and K. Nomura, “Bose-Mesner algebra related with type II matrices and spin models,” J. Algebraic Combin. 8 (1998), 39-72.
10. K. Nomura, “Type II matrices of size five,” Graphs Combin. 15 (1999), 79-92.
2. E. Bannai and T. Ito, Algebraic Combinatorics. I. Association Schemes, Benjamin/Cummings Publisher Co., Inc., Menlo Park, Calif., 1984.
3. A.E. Brouwer, “Strongly regular graphs,” in The CRC Handbook of Combinatorial Designs, C.J. Colbourn and J.H. Dinitz (Eds.), CRC Press, Boca Raton, 1996, pp. 667-683.
4. C.D. Godsil, Algebraic Combinatorics, Chapman & Hall, New York, 1993.
5. C.D. Godsil, “Type II matrices and Jones pairs,”
2001. Preprints.
6. C.D. Godsil and A. Chan, “Strongly regular graphs and type II matrices,”
2001. Preprints.
7. R. Hosoya and H. Suzuki, “Type II matrices and their Bose-Mesner algebras,” J. Algebraic Combin. 17 (2003), 19-37.
8. F. Jaeger, “Strongly regular graphs and spin models for the Kauffman polynomial,” Geom. Dedicata 44 (1992), 23-52.
9. F. Jaeger, M. Matsumoto, and K. Nomura, “Bose-Mesner algebra related with type II matrices and spin models,” J. Algebraic Combin. 8 (1998), 39-72.
10. K. Nomura, “Type II matrices of size five,” Graphs Combin. 15 (1999), 79-92.