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In this paper, we study the $q$-distance matrix for a distance-regular graphand show that the $q$-distance matrix of a distance-regular graph withclassical parameters ($D, q, \alpha, \beta$) has exactly three distincteigenvalues, of which one is zero. Moreover, we study distance-regular graphswhose $q$-distance matrix has exactly one positive eigenvalue.

Distance-regular graphs with exactly one positive $q$-distance eigenvalue