Yes, the velocity of a photon in a vacuum, commonly denoted as "c," is independent of its wavelength. According to the theory of special relativity, the speed of light in a vacuum is a fundamental constant of nature, and it is the same for all photons regardless of their wavelength or frequency.
In other words, whether a photon has a longer wavelength (lower frequency) or a shorter wavelength (higher frequency), its velocity remains constant at the speed of light, approximately 299,792,458 meters per second (or about 186,282 miles per second).
It's important to note that although the velocity of a photon is constant, its energy and momentum are related to its frequency or wavelength through the equations E = hf (where E is energy, h is Planck's constant, and f is frequency) and p = h/λ (where p is momentum and λ is wavelength).