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About the shortest chain between two vertices in a quasi strongly connected digraph with a potential

✍ Scribed by Jean-Pierre Barthelemy


Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
370 KB
Volume
34
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis


A closed form solution is provided for the length, relatively between two vertices of a quasi strongly connected digraph. to a potential Cr, of a chain

I. Detidtions and nobtion!!i

Let G = (V, A) denote a finite connected digraph without loop; V is the set of vertices and A the set of arcs. A chain between two vertices x and y is a sequence x = x0 x1 . . l x,,=y such that (q,q+l)~A or (x,+l,x&A, Niin-1. In particular a path from x to y is a clrain between x and y.

A pomtial 8 on G is a real valued function defined on V such that: