Abstract
In this paper we consider a strongly regular graph, G, whose adjacency matrix A has three distinct eigenvalues, and a particular real three dimensional Euclidean Jordan subalgebra with rank three of the Euclidean algebra of real symmetric matrices of order n, with the product and the inner product being the Jordan product and the usual trace of matrices, respectively. Next, we compute the unique Jordan frame \(\mathscr {B}\) associated to A and we consider particular alternating Hadamard series constructed from the idempotents of \(\mathscr {B}\). Finally, by the analysis of the spectra of the sums of these alternating Hadamard series we deduce some theorems over the parameters of a strongly regular graph.
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Acknowledgements
Luís Vieira was supported by the European Regional Development Fund Through the program COMPETE and by the Portuguese Government through the FCT - Fundação para a Ciência e a Tecnologia under the project PEst- C/MAT/UI0144/2013.
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de Almeida Vieira, L.A., Mano, V.M. (2017). Alternating Hadamard Series and Some Theorems on Strongly Regular Graphs. In: Pinto, A., Zilberman, D. (eds) Modeling, Dynamics, Optimization and Bioeconomics II. DGS 2014. Springer Proceedings in Mathematics & Statistics, vol 195. Springer, Cham. https://doi.org/10.1007/978-3-319-55236-1_23
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DOI: https://doi.org/10.1007/978-3-319-55236-1_23
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