If you say you're a PhD student in this and that department, I don't think this would imply anything about your supervisor having contributed to it. If you're the author of the paper, it's your work. In the Acknowledgements section, you could mention your suprvisor and thank for stimulating discussions or something along these lines, but I don't think this is really necessary.
(at least that's the impression I got from reading published journal articles by PhD students)