which relationship satisfied distance traveled by a single photon.How?
As far as we can tell, there is no distance limit on a photon's travel - with the caveat that physical objects, electromagnetic fields and gravity may interfere with them
Hubble has been observing single photon events in deep space vacuum for many years now, where the photons were emitted billions of years ago and are still travelling at the same absolute wavelength. We may see this as a red or blue-shifted wavelength depending on our relative travel to the original emitter.
This means these photons have travelled billions of light-years with no obvious loss of energy.
I agree with Dr Ian Proffitt that there is no limit on travelling of photons. Only thing is that gravity may affect depending on the condition and its magnitude.
Yes; it only "dies" or is otherwise modified if it interacts with something. Of course there is no such thing as perfect vacuum over all of space.
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