TITLE:
Binomial Hadamard Series and Inequalities over the Spectra of a Strongly Regular Graph
AUTHORS:
Luís Vieira
KEYWORDS:
Euclidean Jordan Algebras, Graph Theory, Strongly Regular Graphs
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.9,
September
28,
2018
ABSTRACT: Let G be a primitive strongly regular graph of order n and A is adjacency matrix.
In this paper we first associate to A a real 3-dimensional Euclidean Jordan
algebra with rank three spanned by In and the natural powers of A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix of
order n. Next we consider a basis that is a Jordan frame of . Finally,
by an algebraic asymptotic analysis of the second spectral decomposition of
some Hadamard series associated to A we establish some inequalities over the
spectra and over the parameters of a strongly regular graph.