degree from the University of Zagreb, in the area of theoretical organic chemistry.
From 1977 he worked at the University of Kragujevac, eventually becoming a full research professor in 1982.
Gutman is known for his work in chemical graph theory and topological descriptors.
In mathematics he introduced the notion of graph energy, a concept originating from theoretical chemistry.
[7] Gutman is a collaborator on the Lexicon of Danube Croats for Croatian Academic Society 'HAD' in Subotica.