A Spectral Equivalent Condition of the $P$-Polynomial Property for Association Schemes
Keywords: P-polynomial association scheme, distance-regular graph, graph spectrum, spectral excess theorem, predistance polynomial
AbstractWe 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.