In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on graphs possessing
quantum decomposition (QD graphs) have been calculated by a new method based on spectral
distribution associated to their adjacency matrix. Here in this paper, it is shown
that the continuous-time quantum walk on any arbitrary graph can be investigated by
spectral distribution method, simply by using Krylov subspace-Lanczos algorithm to
generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal
polynomials. Also new type of graphs possessing generalized quantum decomposition
have been introduced, where this is achieved simply by relaxing some of the constrains
imposed on QD graphs and it is shown that both in QD and GQD graphs, the unit vectors
of strata are identical with the orthonormal basis produced by Lanczos algorithm.
Moreover, it is shown that probability amplitude of observing walk at a given vertex
is proportional to its coefficient in the corresponding unit vector of its stratum,
and it can be written in terms of the amplitude of its stratum. Finally the capability
of Lanczos-based algorithm for evaluation of walk on arbitrary graphs (GQD or non-QD
types), has been tested by calculating the probability amplitudes of quantum walk
on some interesting finite (infinite) graph of GQD type and finite (infinite) path
graph of non-GQD type, where the asymptotic behavior of the probability amplitudes
at infinite limit of number of vertices, are in agreement with those of central limit
theorem of Ref.\cite{nko}.