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Submitted
Aug 5, 2020
Published
Dec 29, 2016
GEODESY OF GRAPHS
Corresponding Author(s) : Luong Quoc Tuyen
lqtuyen@ued.udn.vn
UED Journal of Social Sciences, Humanities and Education,
Vol. 6 No. 4 (2016): UED JOURNAL OF SOCIAL SCIENCES, HUMANITIES AND EDUCATION
Abstract
In this article, we firstly prove that the length of every piecewise linear path in a metric space X does not depend on the partitions of section [a,b], and affine mappings ck defined on section [tk, tk+1]. Secondly, we prove that with any x and y in a metric space X, there exists a piecewise linear path joining x to y. Thirdly, we prove that the formula
d(x,y) = inf {l(c): c is a piecewise linear path joining x to y}
is a metric on X. Finally, we prove that with the metric defined above, (X,d) is a geodesic metric space
Keywords
graph; metric space; geodesic metric space; geodesic path; piecewise linear path; affine mapping.
Luong Quoc Tuyen, & Le Thi Thu Nguyet. (2016). GEODESY OF GRAPHS. UED Journal of Social Sciences, Humanities and Education, 6(4), 17-26. https://doi.org/10.47393/jshe.v6i4.670
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References
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