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Graph topologies induced by edge lengths
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Georgakopoulos, Agelos (2011) Graph topologies induced by edge lengths. Discrete Mathematics, Vol.311 (No.15). pp. 1523-1542. doi:10.1016/j.disc.2011.02.012 ISSN 0012-365X.
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Official URL: http://dx.doi.org/10.1016/j.disc.2011.02.012
Abstract
Let G be a graph each edge e of which is given a length ℓ(e). This naturally induces a distance dℓ(x,y) between any two vertices x,y, and we let |G|ℓ denote the completion of the corresponding metric space. It turns out that several well-studied topologies on infinite graphs are special cases of |G|ℓ. Moreover, it seems that |G|ℓ is the right setting for studying various problems. The aim of this paper is to introduce |G|ℓ, providing basic facts, motivating examples and open problems, and indicate possible applications.
Parts of this work suggest interactions between graph theory and other fields, including algebraic topology and geometric group theory.
Keywords
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Discrete Mathematics | ||||
Publisher: | Elsevier BV | ||||
ISSN: | 0012-365X | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.311 | ||||
Number: | No.15 | ||||
Page Range: | pp. 1523-1542 | ||||
DOI: | 10.1016/j.disc.2011.02.012 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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