Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 1, pp. 27-31 (2002)

Configuration Spaces of Weighted Graphs in High Dimensional Euclidean Spaces

Olivier Mermoud, Marcel Steiner

Département de Génie Mécanique, ICAP-LICP, EPFL, CH-1015 Lausanne, e-mail:; Département de Mathématiques, EPFL, CH-1015 Lausanne, e-mail:

Abstract: Let ${\cal{G}} = (V, E, d)$ be any connected weighted graph which admits not only degenerated realisations in the $n$-dimensional Euclidean space. Its configuration space is always homeomorphic to a $({1\over 2} n(n+1) - e)$-dimensional sphere, where $n$ is the number of vertices minus one and $e$ the number of edges.

Keywords: weighted graph; realisations in $\bbf R^n$; distance-preserving embeddings of graphs in Euclidean space

Classification (MSC2000): 52A37; 05C62

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