(Abridged abstract) We explore the formation of ultra-massive (M_{rm WD} gtrsim 1.05 M_sun$), carbon-oxygen core white dwarfs resulting from single stellar evolution. We also study their evolutionary and pulsational properties and compare them with those of the ultra-massive white dwarfs with oxygen-neon cores resulting from carbon burning in single progenitor stars, and with binary merger predictions. We consider two single-star evolution scenarios for the formation of ultra-massive carbon-oxygen core white dwarfs that involve rotation of the degenerate core after core helium burning and reduced mass-loss rates in massive asymptotic giant-branch stars. We compare our findings with the predictions from ultra-massive white dwarfs resulting from the merger of two equal-mass carbon-oxygen core white dwarfs, by assuming complete mixing between them and a carbon-oxygen core for the merged remnant. The resulting ultra-massive carbon-oxygen core white dwarfs evolve markedly slower than their oxygen-neon counterparts. Our study strongly suggests the formation of ultra-massive white dwarfs with carbon-oxygen core from single stellar evolution. We find that both the evolutionary and pulsation properties of these white dwarfs are markedly different from those of their oxygen-neon core counterparts and from those white dwarfs with carbon-oxygen core that might result from double degenerate mergers. This can eventually be used to discern the core composition of ultra-massive white dwarfs and their formation scenario.
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