I want to know difference between propagation speed and bandwidth in digital communication.I know bandwidth is no of bits in one second and propagation speed of signal is distance traveled by signal is one second.Is there any relation between them or they are totally different.Can anyone tell me exact definition to differentiate these twos.
They are unrelated.
The bandwidth is, as you correctly said, the number of bits per second. The propagation speed is the time until the first bit arrives (this is also called the latency).
Imagine you have an army of snails that can carry SD cards along a straight line. Their propagation speed is very slow, so it takes a long time until a snail arrives after you send it. However, you can send a snail every second, so that after the initial delay your snails deliver one SD card of data every second. That's high bandwidth.