Isometrically Embedded Graphs

Debra L.Boutin1
1Department of Mathematics Hamilton College, Clinton, NY 13323

Abstract

Can an arbitrary graph be embedded in Euclidean space so that the isometry group of its vertex set is precisely its graph automorphism group? This paper gives an affirmative answer, explores the number of dimensions necessary, and classifies the outerplanar graphs that have such an embedding in the plane.