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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/12861

Title: The Group Structure of Pivot and Loop Complementation on Graphs and Set Systems
Authors: Brijder, Robert
Hoogeboom, Hendrik Jan
Issue Date: 2011
Citation: EUROPEAN JOURNAL OF COMBINATORICS, 32(8), p. 1353-1367
Abstract: We study the interplay between the principal pivot transform (pivot) and loop complementation for graphs. This is done by generalizing loop complementation (in addition to pivot) to set systems. We show that the operations together, when restricted to single vertices, form the permutation group S 3 . This leads, e.g., to a normal form for sequences of pivots and loop complementation on graphs. The results have consequences for the operations of local complementation and edge complementation on simple graphs: an alternative proof of a classic result involving local and edge complementation is obtained, and the effect of sequences of local complementations on simple graphs is characterized.
URI: http://hdl.handle.net/1942/12861
DOI: 10.1016/j.ejc.2011.03.002
ISSN: 0195-6698
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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