  Continuous-time quantum walk (CTQW) on a given graph is investigated by using
the techniques of the spectral analysis and inverse Laplace transform of the
Stieltjes function (Stieltjes transform of the spectral distribution)
associated with the graph. It is shown that, the probability amplitude of
observing the CTQW at a given site at time $t$ is related to the inverse
Laplace transformation of the Stieltjes function, namely, one can calculate the
probability amplitudes only by taking the inverse laplace transform of the
function $iG_{\mu}(is)$, where $G_{\mu}(x)$ is the Stieltjes function of the
graph. The preference of this procedure is that, there is no any need to know
the spectrum of the graph
