On the classification of plane graphs representing structurally stable rational Newton flows

Jongen, H.Th. and Jonker, P. and Twilt, F. (1991) On the classification of plane graphs representing structurally stable rational Newton flows. Journal of Combinatorial Theory, Series B, 51 (2). pp. 256-270. ISSN 0021-9800

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Abstract:	We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton's iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles between edges at the same vertex. We derive necessary and sufficient conditions -of purely combinatorial nature- for an arbitrary plane graph in order to be topologically equivalent with a Newton graph. Finally, we analyse the structure of Newton graphs and prove the existence of a polynomial algorithm to recognize such graphs.
Item Type:	Article
Copyright:	© 1991 Elsevier
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Discrete Mathematics and Mathematical Programming (DMMP)
Link to this item:	http://purl.utwente.nl/publications/72943
Official URL:	http://dx.doi.org/10.1016/0095-8956(91)90041-H
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