In this work , analyzing the propagation of electromagnetic waves in the field of gravitational waves , we show the presence and significance of the so called surfing effect for pulsar timing measurements .
It is shown that , due to the transverse nature of gravitational waves , the surfing effect leads to enormous pulsar timing residuals if the speed of gravitational waves is smaller than speed of light .
This fact allows to place significant constraints on parameter \epsilon , which characterizes the relative deviation of the speed of gravitational waves from the speed of light .
We show that the existing constraints from pulsar timing measurements already place stringent limits on \epsilon and consequently on the mass of graviton m _ { g } .
These limits on m _ { g } are three orders of magnitude stronger than the current constraints from Solar System tests .
The current constraints also allow to rule out massive gravitons as possible candidates for cold dark matter in galactic halo .
In the near future , the gravitational wave background from extragalactic super massive black hole binaries , along with the expected sub-microsecond pulsar timing accuracy , will allow to achieve constrains of \epsilon \lesssim 0.4 \% and possibly stronger .