Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648783 | Discrete Mathematics | 2011 | 20 Pages |
Abstract
Let GG be a graph each edge ee of which is given a length ℓ(e)ℓ(e). This naturally induces a distance dℓ(x,y)dℓ(x,y) between any two vertices x,yx,y, and we let |G|ℓ|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|G|ℓ. Moreover, it seems that |G|ℓ|G|ℓ is the right setting for studying various problems. The aim of this paper is to introduce |G|ℓ|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
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Agelos Georgakopoulos,