Does the same music theory apply to the fret board of a mandolin as a guitar? i.e.
a to b is a whole step, b to c is a half step, c to d is a whole step, d to e is a half step, etc.
Where b to c and d to e is always a half step?
I believe it is but I just want validation.
Thanks. 
You are correct about the music theory applying equally to both instruments! One slight issue… you say that “d to e is a half step,” that is not correct. All notes have a whole step between them except for B to C and E to F (both of which are half steps). If you have familiarity with a piano keyboard, it’s easy to visualize those as those notes don’t have the black keys between them.
It’s actually the same on all western instruments, banjo, lute, mandolin, violin, trumpet, tuba, piano, oboe etc…it is what is music or the " theory " that drives it. Congrats you now have a new understanding and view of the world of music, you will never see another instrumentt the same again.