A Spectral Equivalent Condition of the $P$-Polynomial Property for Association Schemes

Hiroshi Nozaki, Hirotake Kurihara


We give two equivalent conditions of the $P$-polynomial property of a symmetric association scheme. The first equivalent condition shows that the $P$-polynomial property is determined only by the first and second eigenmatrices of the symmetric association scheme. The second equivalent condition is another expression of the first using predistance polynomials.


P-polynomial association scheme; distance-regular graph; graph spectrum; spectral excess theorem; predistance polynomial

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