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Article
Integer Functions on the Cycle Space and Edges of a Graph
Graphs and Combinatorics
Document Type
Article
Publication Date
2-1-2010
Disciplines
Abstract
A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any Z-module homomorphism of a graph’s cycle space to Z that satisfies these two properties for all cycles must be such a map induced from an edge direction on the graph. In this paper we will prove a generalization of this theorem and an analogue as well.
Citation Information
Dan Slilaty. "Integer Functions on the Cycle Space and Edges of a Graph" Graphs and Combinatorics Vol. 26 (2010) p. 293 - 299 ISSN: 0911-0119 Available at: http://works.bepress.com/dan_slilaty/14/