Stable Maps from #n(S1×S2) to the Euclidean 3-Space

We introduce a graph associated with any stable map defined from the connected sum # n ( S 1 × S 2 ) of n copies of the product S 1 × S 2 to the Euclidean 3-space. This graph has a weight on each vertex and a pair of weights on each edge, and its properties provide a necessary and sufficient condition to be the graph of a stable map defined from # n ( S 1 × S 2 ) to the Euclidean 3-space.