Admissibility Conditions and Asymptotic Behavior of Strongly Regular Graphs
نویسندگان
چکیده
We consider a strongly regular graph, G, with adjacency matrix A, and associate a three dimensional Euclidean Jordan algebra to A. Then, by considering convergent series of Hadamard powers of the idempotents of the unique complete system of orthogonal idempotents of the Euclidean Jordan algebra associated to A, we establish new admissibility conditions for the existence of strongly regular graphs. Finally, we extract some asymptotic conclusions about the spectrum of G. Keywords-Combinatorial Mathematics, Graph theory, Linear algebra, Symmetric matrices, Linear matrix inequalities.
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