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A graph $\Gamma$ labelled by a set $S$ defines a group $G(\Gamma)$ whosegenerators are the set of labels $S$ and whose relations are all words whichcan be read on closed paths of this graph. We introduce the notion ofaspherical graph and prove that such a graph defines an aspherical grouppresentation. This result generalizes a theorem of Dominik Gruber on graphssatisfying graphical $C(6)$-condition and also allows to get new graphicalconditions of asphericity analogous to some classical conditions.

Asphericity of groups defined by graphs