A generalized representation of the “rectilinear diameter” rule
✍ Scribed by N. K. Bolotin; A. M. Shelomentsev; M. Yu. Tyutyunnikov
- Publisher
- Springer US
- Year
- 1975
- Tongue
- English
- Weight
- 144 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0009-3092
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## Abstract We generalize the concept of the diameter of a graph __G__ = (__N, A__) to allow for location of points not on the nodes. It is shown that there exists a finite set of candidate points which determine this __generalized diameter.__ Given the matrix of shortest paths, an __o__ (|__A__|^2
A graph is called a generalized S-graph if for every vertex v of G there exists exactly one vertex which is more remote from v than every vertex adjacent to v. A generalized S-graph of diameter 3 is called reducible if there is a pair of diametrical vertices v and t~ such that G-{u, ~} is also a gen