V članku razširimo študij totalnih grafov ▫$\tau(R)$▫ na nekomutativne končne kolobarje ▫$R$▫. Dokažemo, da je ▫$\tau(R)$▫ povezan graf natanko tedaj, ko ▫$R$▫ ni lokalni kolobar in preverimo, da je ...v tem primeru ▫$\tau(R)▫$ vedno hamiltonski graf. Najdemo tudi zgornjo mejo za dominacijsko število grafa ▫$\tau(R)$▫ za vse končne kolobarje ▫$R$▫.
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