A Topological Formula for the Variations of Vertex-Potentials in Networks

Kimio SATO  Norio NISHIZUKA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E75-A   No.7   pp.954-956
Publication Date: 1992/07/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Graphs, Networks and Matroids
Keyword: 
vertex-potential,  network,  weight,  tree and 2-tree product sums,  

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Summary: 
A formula for the variations in vertex-potentials caused by an increase of an edge-weight is derived using topological methods. This formula can be expressed in terms of the increase of the weight and the potential differences between two vertices joined by the edge with respect to three ordered vertex-pairs in the original network before the weight is increased.