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THE WRITHE OF ORIENTED POLYGONAL GRAPHS

CHRISTIAN LAING

Department of Mathematics, Florida State University, 208 Love Building Tallahassee FL 32306-4510, USA

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and

DE WITT SUMNERS

Department of Mathematics, Florida State University, 208 Love Building Tallahassee FL 32306-4510, USA

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https://doi.org/10.1142/S0218216508006786Cited by:6 (Source: Crossref)

Abstract

Given an edge-oriented polygonal graph in ℝ³, we describe a method for computing the writhe as the average of weighted directional writhe numbers of the graph in a few directions. These directions are determined by the graph and the weights are determined by areas of path-connected open regions on the unit sphere. Within each open region, the directional writhe is constant. We obtain a closed formula which extends the formula for the writhe of a polygon in ℝ³, including the important special case of writhe of embedded open arcs.

Keywords:

AMSC: 57M25, 57M27

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