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A total perfect code in\n \n \n $$\\Gamma $$<\/jats:tex-math>\n \n \u0393<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is a subset\n C<\/jats:italic>\n of\n V<\/jats:italic>\n such that every vertex of\n \n \n $$\\Gamma $$<\/jats:tex-math>\n \n \u0393<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is adjacent to exactly one vertex in\n C<\/jats:italic>\n . 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