Signed graphs cospectral with the path

A signed graph Γ is said to be determined by its spectrum if every signed graph with the same spectrum as Γ is switching isomorphic with Γ. Here it is proved that the path P n , interpreted as a signed graph, is determined by its spectrum if and only if n ≡ 0 , 1 , or 2 (mod 4), unless n ∈ { 8 , 13 , 14 , 17 , 29 } , or n = 3 .