In this paper we define the total curvature of a polygonal map from a finite graph G to a Euclidean space En. We characterize for certain G the polygonal maps with minimal total curvature. When G is homeomorphic to a circle the result is the piecewise linear version of the generalized Fenchel theorem on the total curvature of a smooth closed curve in a Euclidean space.
- Total curvature of graphs
ASJC Scopus subject areas
- Geometry and Topology
- Computational Theory and Mathematics