Let Γ be a graph on n vertices, adjacency matrix A, and distinct eigenvalues λ > λ1 > λ2 > · · · > λd. For every k = 0, 1, . . . , d−1, the k-alternating polynomial Pk is defined to be the polynomial of degree k and norm ‖Pk‖∞ = max1≤l≤d{|Pk(λl)|} = 1 that attains maximum value at λ. These polynomials, which may be thought of as the discrete version of the Chebychev ones, were recently used by ...
