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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On isometric embeddings of graphs
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by R. L. Graham and P. M. Winkler PDF
Trans. Amer. Math. Soc. 288 (1985), 527-536 Request permission

Corrigendum: Trans. Amer. Math. Soc. 294 (1986), 379.

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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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 288 (1985), 527-536
  • MSC: Primary 05C10; Secondary 51K99
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0776391-5
  • MathSciNet review: 776391