The on-surface reactions of 10-bromo-10'-(2,6-dimethylpheny1)-9,9'-bianthracene on Au(111) have been investigated by scanning tunneling microscopy and spectroscopy, complemented by theoretical calculations. The reactions afford the synthesis of two open-shell nanographenes (1a and 1b) exhibiting different scenarios of all-carbon magnetism. la, an all-benzenoid nanographene with triangulene-like termini, contains a high proportion of zigzag edges which endows it with a low frontier gap and edge-localized states. The dominant reaction product, 1b, is a non-benzenoid nanographene consisting of a single pentagonal ring in a benzenoid framework. The presence of this non-benzenoid topological defect, which alters the bond connectivity in the hexagonal lattice, results in a non-Kekule nanographene with an unpaired spin, which is detected as a Kondo resonance.