A graphic designer who taught at two Big Apple colleges was found dead with bruising to her neck inside her apartment about a block from Brooklyn’s Greenwood Cemetery Tuesday – and investigators are probing her death as suspicious, cops and sources said.

Claudia Brandenburg, 58, was lying in bed unconscious and unresponsive inside her co-op apartment on Prospect Park West near 17th Street when her husband found her and called 911 around 7:45 a.m., authorities and sources said.

Brandenburg — a part-time assistant professor at the New School’s Parsons School for Design since 2002, and an adjunct professor at NYU Steinhardt School of Art and Art Professions since 2015, according to her LinkedIn page — was pronounced dead by first responders, police said.

Claudia Brandenburg, 58, was foun

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