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We define an Artin group of circuit rank 1 as an Artin group based on a connected graph with fundamental group a free group of rank 1. For an Artin group  G  of circuit rank 1 the Bieri–Neumann–Renz–Strebel invariantΣ  1    (  G  ,  ℤ  )${\Sigma ^1(G, \mathbb {Z})}$    is calculated.

The Σ 1 -invariant for Artin groups of circuit rank 1