  The continuous-time quantum walk on the underlying graphs of association
schemes have been studied, via the algebraic combinatorics structures of
association schemes, namely semi-simple modules of their Bose-Mesner and
(reference state dependent) Terwilliger algebras. By choosing the (walk)
starting site as a reference state, the Terwilliger algebra connected with this
choice turns the graph into the metric space, hence stratifies the graph into a
(d+1) disjoint union of strata, where the amplitudes of observing the
continuous-time quantum walk on all sites belonging to a given stratum are the
same. In graphs of association schemes with known spectrum, the transition
amplitudes and average probabilities are given in terms of dual eigenvalues of
association schemes. As most of association schemes arise from finite groups,
hence the continuous-time walk on generic group association schemes have been
studied in great details, where the transition amplitudes are given in terms of
characters of groups. Further investigated examples are the walk on graphs of
association schemes of symmetric $S_n$, Dihedral $D_{2m}$ and cyclic groups.
Also, following Ref.\cite{js}, the spectral distributions connected to the
highest irreducible representations of Terwilliger algebras of some rather
important graphs, namely distance regular graphs, have been presented. Then
using spectral distribution, the amplitudes of continuous-time quantum walk on
graphs such as cycle graph $C_n$, Johnson and normal subgroup graphs have been
evaluated. {\bf Keywords: Continuous-time quantum walk, Association scheme,
Bose-Mesner algebra, Terwilliger algebra, Spectral distribution, Distance
regular graph.} {\bf PACs Index: 03.65.Ud}
