GENERA OF THE LINKS DERIVED FROM 2-CONNECTED PLANE GRAPHS

In this paper, we associate a plane graph G with an oriented link by replacing each vertex of G with a special oriented n-tangle diagram. It is shown that such an oriented link has the minimum genus over all orientations of its unoriented version if its associated plane graph G is 2-connected. As a result, the genera of a large family of unoriented links are determined by an explicit formula in terms of their component numbers and the degree sum of their associated plane graphs.

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