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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On isometric embeddings of graphs


Authors: R. L. Graham and P. M. Winkler
Journal: Trans. Amer. Math. Soc. 288 (1985), 527-536
MSC: Primary 05C10; Secondary 51K99
Corrigendum: Trans. Amer. Math. Soc. 294 (1986), 379.
MathSciNet review: 776391
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Abstract: If $ G$ is a finite connected graph with vertex set $ V$ and edge set $ E$, a standard way of defining a distance $ {d_G}$ on $ G$ is to define $ {d_G}(x,y)$ to be the number of edges in a shortest path joining $ x$ and $ y$ in $ V$. If $ (M,{d_M})$ is an arbitrary metric space, then an embedding $ \lambda :V \to M$ is said to be isometric if $ {d_G}(x,y) = {d_M}(\lambda (x),\lambda (y))$ for all $ x,y \in V$. In this paper we will lay the foundation for a theory of isometric embeddings of graphs into cartesian products of metric spaces.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0776391-5
PII: S 0002-9947(1985)0776391-5
Article copyright: © Copyright 1985 American Mathematical Society