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Generalized Krein Parameters of a Strongly Regular Graph

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DOI: 10.4236/am.2015.61005    5,503 Downloads   6,246 Views   Citations

ABSTRACT

We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Vieira, L. and Mano, V. (2015) Generalized Krein Parameters of a Strongly Regular Graph. Applied Mathematics, 6, 37-45. doi: 10.4236/am.2015.61005.

References

[1] McCrimmon, K. (1978) Jordan Algebras and Their Applications. Bulletin of the American Mathematical Society, 84, 612-627.
http://dx.doi.org/10.1090/S0002-9904-1978-14503-0
[2] Jordan, P., Neuman, J.V. and Wigner, E. (1934) On an Algebraic Generalization of the Quantum Mechanical Formalism. Annals of Mathematics, 35, 29-64.
http://dx.doi.org/10.2307/1968117
[3] Massan, H. and Neher, E. (1998) Estimation and Testing for Lattice Conditional Independence Models on Euclidean Jordan Algebras. Annals of Statistics, 26, 1051-1082.
http://dx.doi.org/10.1214/aos/1024691088
[4] Faybusovich, L. (1997) Euclidean Jordan Algebras and Interior-Point Algorithms. Positivity, 1, 331-357.
http://dx.doi.org/10.1023/A:1009701824047
[5] Faybusovich, L. (2007) Linear Systems in Jordan Algebras and Primal-Dual Interior-Point Algorithms. Journal of Computational and Applied Mathematics, 86, 149-175.
http://dx.doi.org/10.1016/S0377-0427(97)00153-2
[6] Cardoso, D.M. and Vieira, L.A. (2004) Euclidean Jordan Algebras with Strongly Regular Graphs. Journal of Mathematical Sciences, 120, 881-894.
http://dx.doi.org/10.1023/B:JOTH.0000013553.99598.cb
[7] Koecher, M. (1999) The Minnesota Notes on Jordan Algebras and Their Applications. Krieg, A. and Walcher, S., Eds., Springer, Berlin.
[8] Faraut, J. and Korányi, A. (1994) Analysis on Symmetric Cones. Oxford Science Publications, Oxford.
[9] Godsil, C. and Royle, G. (2001) Algebraic Graph Theory. Springer, Berlin.
http://dx.doi.org/10.1007/978-1-4613-0163-9
[10] van Lint, J.H. and Wilson, R.M. (2004) A Course in Combinatorics. Cambridge University Press, Cambridge.
[11] Scott Jr., L.L. (1973) A Condition on Higman’s Parameters. Notices of the American Mathematical Society, 20, A-97.
[12] Delsarte, Ph., Goethals, J.M. and Seidel, J.J. (1975) Bounds for Systems of Lines and Jacobi Polynomials. Philips Research Reports, 30, 91-105.
[13] Bose, R.C. and Mesner, D.M. (1952) On Linear Associative Algebras Corresponding to Association Schemes of Partially Balanced Designs. The Annals of Mathematical Statistics, 47, 151-184.
[14] Brower, A.E. and Haemers, W.H. (1995) Association Schemes. In: Grahm, R., Grotsel, M. and Lovász. L., Eds., Handbook of Combinatorics, Elsevier, Amsterdam, 745-771.

  
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