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The existence of basket, flat plumbing and flat plumbing basket surfaces of alink was first proven from a braid representative of the link. In the presentarticle, we show the existence of such surfaces from an induced graph of thelink. Consequently, we define the basket number, flat plumbing number and flatplumbing basket number of a link. Then we provide several upper bounds forthese plumbing numbers and study the relation between these plumbing numbersand the genera of links.

An alternating labeling on a spanning tree of Seifert graphs and applications in knot theory