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G n B, C P,, then we say that G is aflat vertex graph. For two spatial graphs G and G', if there exists an isotopy h,:R3 + R3 t E [0,1] such that h, = id *Dedicated to Professor Fujitsugu Hosokawa on his sixtieth birthday.

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The linear skein theory for the Kauffman bracket was introduced by Lickorish [11,12]. It gives an elementary construction of quantum SU(2) invariant of 3-manifolds. In this paper we prove basic properties of the linear skein theory for quantum SU(3) invariant. By using them we give an elementary construction of quantum SU(3) invariant of 3-manifolds and prove topological invariance of the invariant along the construction.