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Camacho, Sad and Lins Neto showed that every holomorphic vector field de fined in C2 with an isolated singularity (the origin o of C2) has a complex analytic subvariety passing through its singularity invariant by the vector field. The subva riety is called a separatrix of the vector field (see [1]). Since the separatrices are analytic subvarieties of C2 (i.e., plane curves), the intersection between a small S3 around the origin and the separatrices is a graph link. So this link is represented by a graph called a splice diagram. These facts motivate us to define certain topolog ical invariants around an isolated singularity of a holomorphic vector field in C2. In fact, we obtaind in [10] and [11] certain topological invariants from the above intersection. So our invariants are induced from the graph link appearing in the intersection and we used the splice diagram to get the invariants. We saw that a splice diagram representing the above graph link is one of the topological invariants of the holomorphic vector field around the singularity (see Theorem A in [10]). In this paper, we first pay attention to the multiple graph link and give an answer to the following question:

Graph link invariants of isolated singularities of holomorphic vector fields in C<sup>2</sup> III